Deck 14: Section 5: Multiple Integration

ملء الشاشة (f)
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سؤال
Set up a double integral that gives the area of the surface of the graph of f over the region R. <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
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سؤال
Find the area of the portion of the surface <strong>Find the area of the portion of the surface   that lies above the region   . Round your answer to two decimal places.</strong> A) 144.00 B) 118.44 C) 904.78 D) 452.39 E) 1,421.22 <div style=padding-top: 35px> that lies above the region <strong>Find the area of the portion of the surface   that lies above the region   . Round your answer to two decimal places.</strong> A) 144.00 B) 118.44 C) 904.78 D) 452.39 E) 1,421.22 <div style=padding-top: 35px> . Round your answer to two decimal places.

A) 144.00
B) 118.44
C) 904.78
D) 452.39
E) 1,421.22
سؤال
Find the area of the surface of the portion of the plane <strong>Find the area of the surface of the portion of the plane   in the first octant.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> in the first octant.

A) <strong>Find the area of the surface of the portion of the plane   in the first octant.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the area of the surface of the portion of the plane   in the first octant.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the area of the surface of the portion of the plane   in the first octant.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the area of the surface of the portion of the plane   in the first octant.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the area of the surface of the portion of the plane   in the first octant.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the area of the surface given by <strong>Find the area of the surface given by   over the region R.   R: rectangle with vertices  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> over the region R. <strong>Find the area of the surface given by   over the region R.   R: rectangle with vertices  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> R: rectangle with vertices <strong>Find the area of the surface given by   over the region R.   R: rectangle with vertices  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find the area of the surface given by   over the region R.   R: rectangle with vertices  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the area of the surface given by   over the region R.   R: rectangle with vertices  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the area of the surface given by   over the region R.   R: rectangle with vertices  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the area of the surface given by   over the region R.   R: rectangle with vertices  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the area of the surface given by   over the region R.   R: rectangle with vertices  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the area of the surface for the portion of the sphere <strong>Find the area of the surface for the portion of the sphere   inside the cylinder   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> inside the cylinder <strong>Find the area of the surface for the portion of the sphere   inside the cylinder   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Find the area of the surface for the portion of the sphere   inside the cylinder   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the area of the surface for the portion of the sphere   inside the cylinder   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the area of the surface for the portion of the sphere   inside the cylinder   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the area of the surface for the portion of the sphere   inside the cylinder   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the area of the surface for the portion of the sphere   inside the cylinder   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Set up a double integral that gives the area of the surface of the graph of f over the region R. <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Set up a double integral that gives the area of the surface on the graph of <strong>Set up a double integral that gives the area of the surface on the graph of   over the region   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> over the region <strong>Set up a double integral that gives the area of the surface on the graph of   over the region   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Set up a double integral that gives the area of the surface on the graph of   over the region   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Set up a double integral that gives the area of the surface on the graph of   over the region   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Set up a double integral that gives the area of the surface on the graph of   over the region   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Set up a double integral that gives the area of the surface on the graph of   over the region   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Set up a double integral that gives the area of the surface on the graph of   over the region   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the area of the surface given by <strong>Find the area of the surface given by   over the region R.   R: square with vertices  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> over the region R. <strong>Find the area of the surface given by   over the region R.   R: square with vertices  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> R: square with vertices <strong>Find the area of the surface given by   over the region R.   R: square with vertices  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find the area of the surface given by   over the region R.   R: square with vertices  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the area of the surface given by   over the region R.   R: square with vertices  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the area of the surface given by   over the region R.   R: square with vertices  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the area of the surface given by   over the region R.   R: square with vertices  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the area of the surface given by   over the region R.   R: square with vertices  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the area of the surface for the portion of the paraboloid <strong>Find the area of the surface for the portion of the paraboloid   in the first octant.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> in the first octant.

A) <strong>Find the area of the surface for the portion of the paraboloid   in the first octant.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the area of the surface for the portion of the paraboloid   in the first octant.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the area of the surface for the portion of the paraboloid   in the first octant.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the area of the surface for the portion of the paraboloid   in the first octant.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the area of the surface for the portion of the paraboloid   in the first octant.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the area of the portion of the surface <strong>Find the area of the portion of the surface   that lies above the triangular region with vertices   , and   .</strong> A) 4 B) 36 C) 18 D) 162 E) 324 <div style=padding-top: 35px> that lies above the triangular region with vertices <strong>Find the area of the portion of the surface   that lies above the triangular region with vertices   , and   .</strong> A) 4 B) 36 C) 18 D) 162 E) 324 <div style=padding-top: 35px> , and <strong>Find the area of the portion of the surface   that lies above the triangular region with vertices   , and   .</strong> A) 4 B) 36 C) 18 D) 162 E) 324 <div style=padding-top: 35px> .

A) 4
B) 36
C) 18
D) 162
E) 324
سؤال
A company produces a spherical object of radius 17 centimeters. A hole of radius 7 centimeters is drilled through the center of the object. Find the volume of the object.

A) <strong>A company produces a spherical object of radius 17 centimeters. A hole of radius 7 centimeters is drilled through the center of the object. Find the volume of the object.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>A company produces a spherical object of radius 17 centimeters. A hole of radius 7 centimeters is drilled through the center of the object. Find the volume of the object.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>A company produces a spherical object of radius 17 centimeters. A hole of radius 7 centimeters is drilled through the center of the object. Find the volume of the object.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>A company produces a spherical object of radius 17 centimeters. A hole of radius 7 centimeters is drilled through the center of the object. Find the volume of the object.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>A company produces a spherical object of radius 17 centimeters. A hole of radius 7 centimeters is drilled through the center of the object. Find the volume of the object.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the area of the portion of the surface <strong>Find the area of the portion of the surface   that lies above the region   .</strong> A) 72 B) 36 C)   D)   E)   <div style=padding-top: 35px> that lies above the region <strong>Find the area of the portion of the surface   that lies above the region   .</strong> A) 72 B) 36 C)   D)   E)   <div style=padding-top: 35px> .

A) 72
B) 36
C) <strong>Find the area of the portion of the surface   that lies above the region   .</strong> A) 72 B) 36 C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the area of the portion of the surface   that lies above the region   .</strong> A) 72 B) 36 C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the area of the portion of the surface   that lies above the region   .</strong> A) 72 B) 36 C)   D)   E)   <div style=padding-top: 35px>
سؤال
Write a double integral that represents the surface area of <strong>Write a double integral that represents the surface area of   over the region R: triangle with vertices   . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> over the region R: triangle with vertices <strong>Write a double integral that represents the surface area of   over the region R: triangle with vertices   . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places.

A) <strong>Write a double integral that represents the surface area of   over the region R: triangle with vertices   . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Write a double integral that represents the surface area of   over the region R: triangle with vertices   . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Write a double integral that represents the surface area of   over the region R: triangle with vertices   . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Write a double integral that represents the surface area of   over the region R: triangle with vertices   . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Write a double integral that represents the surface area of   over the region R: triangle with vertices   . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
A company produces a spherical object of radius 24 centimeters. A hole of radius 5 centimeters is drilled through the center of the object. Find the outer surface area of the object.

A) <strong>A company produces a spherical object of radius 24 centimeters. A hole of radius 5 centimeters is drilled through the center of the object. Find the outer surface area of the object.</strong> A)   cm<sup>3</sup> B)   cm<sup>3</sup> C)   cm<sup>3</sup> D)   cm<sup>3</sup> E)   cm<sup>3</sup> <div style=padding-top: 35px> cm3
B) <strong>A company produces a spherical object of radius 24 centimeters. A hole of radius 5 centimeters is drilled through the center of the object. Find the outer surface area of the object.</strong> A)   cm<sup>3</sup> B)   cm<sup>3</sup> C)   cm<sup>3</sup> D)   cm<sup>3</sup> E)   cm<sup>3</sup> <div style=padding-top: 35px> cm3
C) <strong>A company produces a spherical object of radius 24 centimeters. A hole of radius 5 centimeters is drilled through the center of the object. Find the outer surface area of the object.</strong> A)   cm<sup>3</sup> B)   cm<sup>3</sup> C)   cm<sup>3</sup> D)   cm<sup>3</sup> E)   cm<sup>3</sup> <div style=padding-top: 35px> cm3
D) <strong>A company produces a spherical object of radius 24 centimeters. A hole of radius 5 centimeters is drilled through the center of the object. Find the outer surface area of the object.</strong> A)   cm<sup>3</sup> B)   cm<sup>3</sup> C)   cm<sup>3</sup> D)   cm<sup>3</sup> E)   cm<sup>3</sup> <div style=padding-top: 35px> cm3
E) <strong>A company produces a spherical object of radius 24 centimeters. A hole of radius 5 centimeters is drilled through the center of the object. Find the outer surface area of the object.</strong> A)   cm<sup>3</sup> B)   cm<sup>3</sup> C)   cm<sup>3</sup> D)   cm<sup>3</sup> E)   cm<sup>3</sup> <div style=padding-top: 35px> cm3
سؤال
Write a double integral that represents the surface area of <strong>Write a double integral that represents the surface area of   over the region R:   . Use a computer algebra system to evaluate the double integral. Round your answer to four decimal places.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> over the region R: <strong>Write a double integral that represents the surface area of   over the region R:   . Use a computer algebra system to evaluate the double integral. Round your answer to four decimal places.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> . Use a computer algebra system to evaluate the double integral. Round your answer to four decimal places.

A) <strong>Write a double integral that represents the surface area of   over the region R:   . Use a computer algebra system to evaluate the double integral. Round your answer to four decimal places.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Write a double integral that represents the surface area of   over the region R:   . Use a computer algebra system to evaluate the double integral. Round your answer to four decimal places.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Write a double integral that represents the surface area of   over the region R:   . Use a computer algebra system to evaluate the double integral. Round your answer to four decimal places.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Write a double integral that represents the surface area of   over the region R:   . Use a computer algebra system to evaluate the double integral. Round your answer to four decimal places.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Write a double integral that represents the surface area of   over the region R:   . Use a computer algebra system to evaluate the double integral. Round your answer to four decimal places.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the area of the portion of the surface <strong>Find the area of the portion of the surface   that lies above the region   . Round your answer to two decimal places.</strong> A) 0.05 B) 2.18 C) 11.97 D) 1.22 E) 12.51 <div style=padding-top: 35px> that lies above the region <strong>Find the area of the portion of the surface   that lies above the region   . Round your answer to two decimal places.</strong> A) 0.05 B) 2.18 C) 11.97 D) 1.22 E) 12.51 <div style=padding-top: 35px> . Round your answer to two decimal places.

A) 0.05
B) 2.18
C) 11.97
D) 1.22
E) 12.51
سؤال
Find the area of the portion of the surface <strong>Find the area of the portion of the surface   that lies above the region   . Round your answer to two decimal places.</strong> A) 9.29 B) 18.58 C) 69.20 D) 5.33 E) 0.65 <div style=padding-top: 35px> that lies above the region <strong>Find the area of the portion of the surface   that lies above the region   . Round your answer to two decimal places.</strong> A) 9.29 B) 18.58 C) 69.20 D) 5.33 E) 0.65 <div style=padding-top: 35px> . Round your answer to two decimal places.

A) 9.29
B) 18.58
C) 69.20
D) 5.33
E) 0.65
سؤال
Find the area of the surface given by <strong>Find the area of the surface given by   over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> over the region R. <strong>Find the area of the surface given by   over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> <strong>Find the area of the surface given by   over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find the area of the surface given by   over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the area of the surface given by   over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the area of the surface given by   over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the area of the surface given by   over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the area of the surface given by   over the region R.    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
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Deck 14: Section 5: Multiple Integration
1
Set up a double integral that gives the area of the surface of the graph of f over the region R. <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)   <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)

A) <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)
B) <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)
C) <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)
D) <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)
E) <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)
2
Find the area of the portion of the surface <strong>Find the area of the portion of the surface   that lies above the region   . Round your answer to two decimal places.</strong> A) 144.00 B) 118.44 C) 904.78 D) 452.39 E) 1,421.22 that lies above the region <strong>Find the area of the portion of the surface   that lies above the region   . Round your answer to two decimal places.</strong> A) 144.00 B) 118.44 C) 904.78 D) 452.39 E) 1,421.22 . Round your answer to two decimal places.

A) 144.00
B) 118.44
C) 904.78
D) 452.39
E) 1,421.22
904.78
3
Find the area of the surface of the portion of the plane <strong>Find the area of the surface of the portion of the plane   in the first octant.</strong> A)   B)   C)   D)   E)   in the first octant.

A) <strong>Find the area of the surface of the portion of the plane   in the first octant.</strong> A)   B)   C)   D)   E)
B) <strong>Find the area of the surface of the portion of the plane   in the first octant.</strong> A)   B)   C)   D)   E)
C) <strong>Find the area of the surface of the portion of the plane   in the first octant.</strong> A)   B)   C)   D)   E)
D) <strong>Find the area of the surface of the portion of the plane   in the first octant.</strong> A)   B)   C)   D)   E)
E) <strong>Find the area of the surface of the portion of the plane   in the first octant.</strong> A)   B)   C)   D)   E)
4
Find the area of the surface given by <strong>Find the area of the surface given by   over the region R.   R: rectangle with vertices  </strong> A)   B)   C)   D)   E)   over the region R. <strong>Find the area of the surface given by   over the region R.   R: rectangle with vertices  </strong> A)   B)   C)   D)   E)   R: rectangle with vertices <strong>Find the area of the surface given by   over the region R.   R: rectangle with vertices  </strong> A)   B)   C)   D)   E)

A) <strong>Find the area of the surface given by   over the region R.   R: rectangle with vertices  </strong> A)   B)   C)   D)   E)
B) <strong>Find the area of the surface given by   over the region R.   R: rectangle with vertices  </strong> A)   B)   C)   D)   E)
C) <strong>Find the area of the surface given by   over the region R.   R: rectangle with vertices  </strong> A)   B)   C)   D)   E)
D) <strong>Find the area of the surface given by   over the region R.   R: rectangle with vertices  </strong> A)   B)   C)   D)   E)
E) <strong>Find the area of the surface given by   over the region R.   R: rectangle with vertices  </strong> A)   B)   C)   D)   E)
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5
Find the area of the surface for the portion of the sphere <strong>Find the area of the surface for the portion of the sphere   inside the cylinder   .</strong> A)   B)   C)   D)   E)   inside the cylinder <strong>Find the area of the surface for the portion of the sphere   inside the cylinder   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Find the area of the surface for the portion of the sphere   inside the cylinder   .</strong> A)   B)   C)   D)   E)
B) <strong>Find the area of the surface for the portion of the sphere   inside the cylinder   .</strong> A)   B)   C)   D)   E)
C) <strong>Find the area of the surface for the portion of the sphere   inside the cylinder   .</strong> A)   B)   C)   D)   E)
D) <strong>Find the area of the surface for the portion of the sphere   inside the cylinder   .</strong> A)   B)   C)   D)   E)
E) <strong>Find the area of the surface for the portion of the sphere   inside the cylinder   .</strong> A)   B)   C)   D)   E)
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6
Set up a double integral that gives the area of the surface of the graph of f over the region R. <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)   <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)

A) <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)
B) <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)
C) <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)
D) <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)
E) <strong>Set up a double integral that gives the area of the surface of the graph of f over the region R.    </strong> A)   B)   C)   D)   E)
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7
Set up a double integral that gives the area of the surface on the graph of <strong>Set up a double integral that gives the area of the surface on the graph of   over the region   .</strong> A)   B)   C)   D)   E)   over the region <strong>Set up a double integral that gives the area of the surface on the graph of   over the region   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Set up a double integral that gives the area of the surface on the graph of   over the region   .</strong> A)   B)   C)   D)   E)
B) <strong>Set up a double integral that gives the area of the surface on the graph of   over the region   .</strong> A)   B)   C)   D)   E)
C) <strong>Set up a double integral that gives the area of the surface on the graph of   over the region   .</strong> A)   B)   C)   D)   E)
D) <strong>Set up a double integral that gives the area of the surface on the graph of   over the region   .</strong> A)   B)   C)   D)   E)
E) <strong>Set up a double integral that gives the area of the surface on the graph of   over the region   .</strong> A)   B)   C)   D)   E)
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8
Find the area of the surface given by <strong>Find the area of the surface given by   over the region R.   R: square with vertices  </strong> A)   B)   C)   D)   E)   over the region R. <strong>Find the area of the surface given by   over the region R.   R: square with vertices  </strong> A)   B)   C)   D)   E)   R: square with vertices <strong>Find the area of the surface given by   over the region R.   R: square with vertices  </strong> A)   B)   C)   D)   E)

A) <strong>Find the area of the surface given by   over the region R.   R: square with vertices  </strong> A)   B)   C)   D)   E)
B) <strong>Find the area of the surface given by   over the region R.   R: square with vertices  </strong> A)   B)   C)   D)   E)
C) <strong>Find the area of the surface given by   over the region R.   R: square with vertices  </strong> A)   B)   C)   D)   E)
D) <strong>Find the area of the surface given by   over the region R.   R: square with vertices  </strong> A)   B)   C)   D)   E)
E) <strong>Find the area of the surface given by   over the region R.   R: square with vertices  </strong> A)   B)   C)   D)   E)
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9
Find the area of the surface for the portion of the paraboloid <strong>Find the area of the surface for the portion of the paraboloid   in the first octant.</strong> A)   B)   C)   D)   E)   in the first octant.

A) <strong>Find the area of the surface for the portion of the paraboloid   in the first octant.</strong> A)   B)   C)   D)   E)
B) <strong>Find the area of the surface for the portion of the paraboloid   in the first octant.</strong> A)   B)   C)   D)   E)
C) <strong>Find the area of the surface for the portion of the paraboloid   in the first octant.</strong> A)   B)   C)   D)   E)
D) <strong>Find the area of the surface for the portion of the paraboloid   in the first octant.</strong> A)   B)   C)   D)   E)
E) <strong>Find the area of the surface for the portion of the paraboloid   in the first octant.</strong> A)   B)   C)   D)   E)
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10
Find the area of the portion of the surface <strong>Find the area of the portion of the surface   that lies above the triangular region with vertices   , and   .</strong> A) 4 B) 36 C) 18 D) 162 E) 324 that lies above the triangular region with vertices <strong>Find the area of the portion of the surface   that lies above the triangular region with vertices   , and   .</strong> A) 4 B) 36 C) 18 D) 162 E) 324 , and <strong>Find the area of the portion of the surface   that lies above the triangular region with vertices   , and   .</strong> A) 4 B) 36 C) 18 D) 162 E) 324 .

A) 4
B) 36
C) 18
D) 162
E) 324
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11
A company produces a spherical object of radius 17 centimeters. A hole of radius 7 centimeters is drilled through the center of the object. Find the volume of the object.

A) <strong>A company produces a spherical object of radius 17 centimeters. A hole of radius 7 centimeters is drilled through the center of the object. Find the volume of the object.</strong> A)   B)   C)   D)   E)
B) <strong>A company produces a spherical object of radius 17 centimeters. A hole of radius 7 centimeters is drilled through the center of the object. Find the volume of the object.</strong> A)   B)   C)   D)   E)
C) <strong>A company produces a spherical object of radius 17 centimeters. A hole of radius 7 centimeters is drilled through the center of the object. Find the volume of the object.</strong> A)   B)   C)   D)   E)
D) <strong>A company produces a spherical object of radius 17 centimeters. A hole of radius 7 centimeters is drilled through the center of the object. Find the volume of the object.</strong> A)   B)   C)   D)   E)
E) <strong>A company produces a spherical object of radius 17 centimeters. A hole of radius 7 centimeters is drilled through the center of the object. Find the volume of the object.</strong> A)   B)   C)   D)   E)
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12
Find the area of the portion of the surface <strong>Find the area of the portion of the surface   that lies above the region   .</strong> A) 72 B) 36 C)   D)   E)   that lies above the region <strong>Find the area of the portion of the surface   that lies above the region   .</strong> A) 72 B) 36 C)   D)   E)   .

A) 72
B) 36
C) <strong>Find the area of the portion of the surface   that lies above the region   .</strong> A) 72 B) 36 C)   D)   E)
D) <strong>Find the area of the portion of the surface   that lies above the region   .</strong> A) 72 B) 36 C)   D)   E)
E) <strong>Find the area of the portion of the surface   that lies above the region   .</strong> A) 72 B) 36 C)   D)   E)
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13
Write a double integral that represents the surface area of <strong>Write a double integral that represents the surface area of   over the region R: triangle with vertices   . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places.</strong> A)   B)   C)   D)   E)   over the region R: triangle with vertices <strong>Write a double integral that represents the surface area of   over the region R: triangle with vertices   . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places.</strong> A)   B)   C)   D)   E)   . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places.

A) <strong>Write a double integral that represents the surface area of   over the region R: triangle with vertices   . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places.</strong> A)   B)   C)   D)   E)
B) <strong>Write a double integral that represents the surface area of   over the region R: triangle with vertices   . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places.</strong> A)   B)   C)   D)   E)
C) <strong>Write a double integral that represents the surface area of   over the region R: triangle with vertices   . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places.</strong> A)   B)   C)   D)   E)
D) <strong>Write a double integral that represents the surface area of   over the region R: triangle with vertices   . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places.</strong> A)   B)   C)   D)   E)
E) <strong>Write a double integral that represents the surface area of   over the region R: triangle with vertices   . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places.</strong> A)   B)   C)   D)   E)
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14
A company produces a spherical object of radius 24 centimeters. A hole of radius 5 centimeters is drilled through the center of the object. Find the outer surface area of the object.

A) <strong>A company produces a spherical object of radius 24 centimeters. A hole of radius 5 centimeters is drilled through the center of the object. Find the outer surface area of the object.</strong> A)   cm<sup>3</sup> B)   cm<sup>3</sup> C)   cm<sup>3</sup> D)   cm<sup>3</sup> E)   cm<sup>3</sup> cm3
B) <strong>A company produces a spherical object of radius 24 centimeters. A hole of radius 5 centimeters is drilled through the center of the object. Find the outer surface area of the object.</strong> A)   cm<sup>3</sup> B)   cm<sup>3</sup> C)   cm<sup>3</sup> D)   cm<sup>3</sup> E)   cm<sup>3</sup> cm3
C) <strong>A company produces a spherical object of radius 24 centimeters. A hole of radius 5 centimeters is drilled through the center of the object. Find the outer surface area of the object.</strong> A)   cm<sup>3</sup> B)   cm<sup>3</sup> C)   cm<sup>3</sup> D)   cm<sup>3</sup> E)   cm<sup>3</sup> cm3
D) <strong>A company produces a spherical object of radius 24 centimeters. A hole of radius 5 centimeters is drilled through the center of the object. Find the outer surface area of the object.</strong> A)   cm<sup>3</sup> B)   cm<sup>3</sup> C)   cm<sup>3</sup> D)   cm<sup>3</sup> E)   cm<sup>3</sup> cm3
E) <strong>A company produces a spherical object of radius 24 centimeters. A hole of radius 5 centimeters is drilled through the center of the object. Find the outer surface area of the object.</strong> A)   cm<sup>3</sup> B)   cm<sup>3</sup> C)   cm<sup>3</sup> D)   cm<sup>3</sup> E)   cm<sup>3</sup> cm3
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15
Write a double integral that represents the surface area of <strong>Write a double integral that represents the surface area of   over the region R:   . Use a computer algebra system to evaluate the double integral. Round your answer to four decimal places.</strong> A)   B)   C)   D)   E)   over the region R: <strong>Write a double integral that represents the surface area of   over the region R:   . Use a computer algebra system to evaluate the double integral. Round your answer to four decimal places.</strong> A)   B)   C)   D)   E)   . Use a computer algebra system to evaluate the double integral. Round your answer to four decimal places.

A) <strong>Write a double integral that represents the surface area of   over the region R:   . Use a computer algebra system to evaluate the double integral. Round your answer to four decimal places.</strong> A)   B)   C)   D)   E)
B) <strong>Write a double integral that represents the surface area of   over the region R:   . Use a computer algebra system to evaluate the double integral. Round your answer to four decimal places.</strong> A)   B)   C)   D)   E)
C) <strong>Write a double integral that represents the surface area of   over the region R:   . Use a computer algebra system to evaluate the double integral. Round your answer to four decimal places.</strong> A)   B)   C)   D)   E)
D) <strong>Write a double integral that represents the surface area of   over the region R:   . Use a computer algebra system to evaluate the double integral. Round your answer to four decimal places.</strong> A)   B)   C)   D)   E)
E) <strong>Write a double integral that represents the surface area of   over the region R:   . Use a computer algebra system to evaluate the double integral. Round your answer to four decimal places.</strong> A)   B)   C)   D)   E)
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16
Find the area of the portion of the surface <strong>Find the area of the portion of the surface   that lies above the region   . Round your answer to two decimal places.</strong> A) 0.05 B) 2.18 C) 11.97 D) 1.22 E) 12.51 that lies above the region <strong>Find the area of the portion of the surface   that lies above the region   . Round your answer to two decimal places.</strong> A) 0.05 B) 2.18 C) 11.97 D) 1.22 E) 12.51 . Round your answer to two decimal places.

A) 0.05
B) 2.18
C) 11.97
D) 1.22
E) 12.51
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17
Find the area of the portion of the surface <strong>Find the area of the portion of the surface   that lies above the region   . Round your answer to two decimal places.</strong> A) 9.29 B) 18.58 C) 69.20 D) 5.33 E) 0.65 that lies above the region <strong>Find the area of the portion of the surface   that lies above the region   . Round your answer to two decimal places.</strong> A) 9.29 B) 18.58 C) 69.20 D) 5.33 E) 0.65 . Round your answer to two decimal places.

A) 9.29
B) 18.58
C) 69.20
D) 5.33
E) 0.65
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18
Find the area of the surface given by <strong>Find the area of the surface given by   over the region R.    </strong> A)   B)   C)   D)   E)   over the region R. <strong>Find the area of the surface given by   over the region R.    </strong> A)   B)   C)   D)   E)   <strong>Find the area of the surface given by   over the region R.    </strong> A)   B)   C)   D)   E)

A) <strong>Find the area of the surface given by   over the region R.    </strong> A)   B)   C)   D)   E)
B) <strong>Find the area of the surface given by   over the region R.    </strong> A)   B)   C)   D)   E)
C) <strong>Find the area of the surface given by   over the region R.    </strong> A)   B)   C)   D)   E)
D) <strong>Find the area of the surface given by   over the region R.    </strong> A)   B)   C)   D)   E)
E) <strong>Find the area of the surface given by   over the region R.    </strong> A)   B)   C)   D)   E)
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