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Stewart_Calc_7ET ch15sec09
MULTIPLE CHOICE
1. Use spherical coordinates.
Evaluate , where is the ball with center the origin and radius .
a.
b.
c.
d.
e.
None of these
2. Use spherical coordinates to evaluate where B is the ball
a.
512
b.
8
c.
64
d.
1024
3. Find the mass of a solid hemisphere of radius 5 if the mass density at any point on the solid is
directly proportional to its distance from the base of the solid.
a.
k
b.
k
c.
k
625
4
25
25
4
d.
k
4. Use spherical coordinates to find the moment of inertia of the solid homogeneous hemisphere
of radius and density 1 about a diameter of its base.
a.
205.13
b.
c.
195.22
d.
213.5
e.
198.08
5. The sketch of the solid is given below. Given , write the inequalities that describe it.
a.
None of these
b.
c.
d.
e.
NUMERIC RESPONSE
1. Use spherical coordinate to find the volume above the cone and inside sphere
.
125
4
2. Use spherical coordinates to find the volume of the solid that lies within the sphere
above the xy-plane and below the cone . Round the answer to
two decimal places.
3. Use cylindrical coordinates to evaluate the triple integral
where E is the solid that lies between the sphere and in the
first octant.
SHORT ANSWER
1. Identify the surface with equation
2. Identify the surface with equation
3. Identify the surface with equation
4. Find the moment of inertia with respect to a diameter of the base of a solid hemisphere of
radius 3 with constant mass density function
