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Deck 12: Extension C: Multiple Integrals
ملء الشاشة (f)
سؤال
A swimming pool is circular with a 
-ft diameter.The depth is constant along east-west lines and increases linearly from 
ft at the south end to 
ft at the north end.Find the volume of water in the pool.
A)
B)
C)
D)
E)
-ft diameter.The depth is constant along east-west lines and increases linearly from ft at the south end to ft at the north end.Find the volume of water in the pool.A)
B)
C)
D)
E)
سؤال
Use a double integral to find the area of the region R where R is bounded by the circle 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Determine whether to use polar coordinates or rectangular coordinates to evaluate the integral 
,where f is a continuous function.Then write an expression for the (iterated)integral. 
,where f is a continuous function.Then write an expression for the (iterated)integral. سؤال
Use polar coordinates to find the volume of the solid under the paraboloid 
and above the disk 
A)
B)
C)
D)
E)
and above the disk A)
B)
C)
D)
E)
سؤال
Use polar coordinates to evaluate. 
سؤال
Use polar coordinates to find the volume of the sphere of radius 
Round to two decimal places.
A)
B)
C)
D)
E)
Round to two decimal places.A)
B)
C)
D)
E)
سؤال
Use polar coordinates to find the volume of the solid bounded by the paraboloid 
and the plane 
A)
B)
C)
D)
E)
and the plane A)
B)
C)
D)
E)
سؤال
An agricultural sprinkler distributes water in a circular pattern of radius 
ft.It supplies water to a depth of 
feet per hour at a distance of 
feet from the sprinkler.What is the total amount of water supplied per hour to the region inside the circle of radius 
feet centered at the sprinkler?
ft.It supplies water to a depth of feet per hour at a distance of feet from the sprinkler.What is the total amount of water supplied per hour to the region inside the circle of radius feet centered at the sprinkler? سؤال
A cylindrical drill with radius 
is used to bore a hole through the center of a sphere of radius 
Find the volume of the ring-shaped solid that remains.Round the answer to the nearest hundredth.
is used to bore a hole through the center of a sphere of radius Find the volume of the ring-shaped solid that remains.Round the answer to the nearest hundredth. سؤال
Evaluate the iterated integral by converting to polar coordinates.Round the answer to two decimal places. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Evaluate the integral 
,where R is the annular region bounded by the circles 
and 
by changing to polar coordinates.
,where R is the annular region bounded by the circles and by changing to polar coordinates.
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ملء الشاشة (f)
Deck 12: Extension C: Multiple Integrals
1
A swimming pool is circular with a -ft diameter.The depth is constant along east-west lines and increases linearly from ft at the south end to ft at the north end.Find the volume of water in the pool.
A)
B)
C)
D)
E)
-ft diameter.The depth is constant along east-west lines and increases linearly from ft at the south end to ft at the north end.Find the volume of water in the pool.A)
B)
C)
D)
E)
2
Use a double integral to find the area of the region R where R is bounded by the circle
A)
B)
C)
D)
A)
B)
C)
D)
3
Determine whether to use polar coordinates or rectangular coordinates to evaluate the integral ,where f is a continuous function.Then write an expression for the (iterated)integral.
,where f is a continuous function.Then write an expression for the (iterated)integral. Polar, 
4
Use polar coordinates to find the volume of the solid under the paraboloid and above the disk
A)
B)
C)
D)
E)
and above the disk A)
B)
C)
D)
E)
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5
Use polar coordinates to evaluate.
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6
Use polar coordinates to find the volume of the sphere of radius Round to two decimal places.
A)
B)
C)
D)
E)
Round to two decimal places.A)
B)
C)
D)
E)
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7
Use polar coordinates to find the volume of the solid bounded by the paraboloid and the plane
A)
B)
C)
D)
E)
and the plane A)
B)
C)
D)
E)
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8
An agricultural sprinkler distributes water in a circular pattern of radius ft.It supplies water to a depth of feet per hour at a distance of feet from the sprinkler.What is the total amount of water supplied per hour to the region inside the circle of radius feet centered at the sprinkler?
ft.It supplies water to a depth of feet per hour at a distance of feet from the sprinkler.What is the total amount of water supplied per hour to the region inside the circle of radius feet centered at the sprinkler? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 11 في هذه المجموعة.
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k this deck
9
A cylindrical drill with radius is used to bore a hole through the center of a sphere of radius Find the volume of the ring-shaped solid that remains.Round the answer to the nearest hundredth.
is used to bore a hole through the center of a sphere of radius Find the volume of the ring-shaped solid that remains.Round the answer to the nearest hundredth. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 11 في هذه المجموعة.
فتح الحزمة
k this deck
10
Evaluate the iterated integral by converting to polar coordinates.Round the answer to two decimal places.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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11
Evaluate the integral ,where R is the annular region bounded by the circles and by changing to polar coordinates.
,where R is the annular region bounded by the circles and by changing to polar coordinates. فتح الحزمة
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