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Stewart_Calc_7ET ch15sec04
MULTIPLE CHOICE
1. Use polar coordinates to find the volume of the solid under the paraboloid and
above the disk .
a.
b.
c.
d.
e.
2. Use polar coordinates to find the volume of the solid bounded by the paraboloid
and the plane .
a.
b.
c.
d.
e.
3. Evaluate the iterated integral by converting to polar coordinates. Round the answer to two
decimal places.
.
a.
b.
c.
d.
e.
4. Use a double integral to find the area of the region R where R is bounded by the circle
a.
b.
36
9
c.
d.
5. Use polar coordinates to find the volume of the sphere of radius . Round to two decimal
places.
a.
b.
c.
d.
e.
6. Use polar coordinates to find the volume of the solid inside the cylinder and
the ellipsoid .
a.
b.
c.
d.
e.
7. 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.
NUMERIC RESPONSE
1. Evaluate the integral by changing to polar coordinates.
18
6
is the region bounded by the semicircle and the -axis.
2. 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.
3. 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?
4. Use polar coordinates to evaluate.
SHORT ANSWER
1. 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.
2. Sketch the region of integration associated with the integral
3. Evaluate the integral , where R is the annular region bounded by the circles
and by changing to polar coordinates.
1 2 3 4 5 6–1–2–3–4–5–6 x
1
2
3
4
5
6
–1
–2
–3
–4
–5
–6
y
4. Evaluate the integral by changing to polar coordinates.
