Exam 12: Extension C: Multiple Integrals

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

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

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

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.

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?

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

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

Use polar coordinates to evaluate.

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.

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

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.