Deck 14: Section 7: Multiple Integration

Question 1

Use spherical coordinates to find the volume of the solid between the spheres and and inside the cone .

A)
B)
C)
D)
E)

Answer 1

Question 2

Use spherical coordinates to find the z coordinate of the center of mass of the solid lying between two concentric hemispheres of radii 4 and 7, and having uniform density k.

A)
B)
C)
D)
E)

Answer 2

Question 3

Use spherical coordinates to find the mass of the sphere and density .

A)
B)
C)
D)
E)

Answer 3

Question 4

Use cylindrical coordinates to find the volume of the solid bounded above by and below by .

A)
B)
C)
D)
E)

Question 5

Evaluate the following iterated integral.

A)
B)
C)
D)
E)

Question 6

Use spherical coordinates to find the z coordinate of the center of mass of the solid lying between two concentric hemispheres of radii 6 and 7, and having uniform density k.

A)
B)
C)
D)
E)

Question 7

Find the "volume" of the "four-dimensional sphere" by evaluating .

A)
B)
C)
D)
E)

Question 8

Use spherical coordinates to find the volume of the solid inside and outside , and above the xy-plane.

A)
B)
C)
D)
E)

Question 9

Evaluate the following iterated integral.

A)
B)
C)
D)
E)

Question 10

Convert the integral below from rectangular coordinates to both cylindrical and spherical coordinates, and evaluate the simpler iterated integral.

A)
B)
C)
D)
E)

Question 11

Convert the integral below from rectangular coordinates to both cylindrical and spherical coordinates, and evaluate the simpler iterated integral.

A)
B)
C)
D)
E)

Question 12

Use spherical coordinates to find the volume of the solid inside the torus given by .

A)
B)
C)
D)
E)

Question 13

Use cylindrical coordinates to find the volume of the solid inside the sphere and above the upper nappe of the cone .

A)
B)
C)
D)
E)

Question 14

Evaluate the iterated integral .

A)
B)
C)
D)
E)

Question 15

Use spherical coordinates to find the mass of the sphere with the given density. The density at any point is proportional to the distance of the point from the z-axis.

A)
B)
C)
D)
E)

Question 16

Use cylindrical coordinates to find the mass of the solid where .

A)
B)
C)
D)
E)

Question 17

Evaluate the following iterated integral.

A)
B)
C)
D)
E)

Question 18

Use cylindrical coordinates to find the volume of the cone where and .

A)
B)
C)
D)
E)

Question 19

Use cylindrical coordinates to find the volume of the solid inside both and .

A)
B)
C)
D)
E)