Deck 12: Extension C: Multiple Integrals

Question 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.

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B)
C)
D)
E)

Answer 1

Question 2

Use a double integral to find the area of the region R where R is bounded by the circle

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B)
C)
D)

Answer 2

Question 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.

Answer 3

Polar,

Question 4

Use polar coordinates to find the volume of the solid under the paraboloid and above the disk

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B)
C)
D)
E)

Question 5

Use polar coordinates to evaluate.

Question 6

Use polar coordinates to find the volume of the sphere of radius Round to two decimal places.

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B)
C)
D)
E)

Question 7

Use polar coordinates to find the volume of the solid bounded by the paraboloid and the plane

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B)
C)
D)
E)

Question 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?

Question 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.

Question 10

Evaluate the iterated integral by converting to polar coordinates.Round the answer to two decimal places.

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B)
C)
D)
E)

Question 11

Evaluate the integral ,where R is the annular region bounded by the circles and by changing to polar coordinates.