Using polar coordinates, evaluate the integral where R is the region

-4.493

The work

2.

By changing to polar coordinates, evaluate the integral
where
D is the disk .
The value is .

27890559.78

The work

3.

Using polar coordinates, evaluate the integral which gives the area which lies
in the first quadrant between the circles and .

100.531

The work

4.

Using polar coordinates, evaluate the integral which gives the area which lies
in the first quadrant below the line y = 10 and between the circles
and
.

34.243

The work

5.

Use the polar coordinates to find the volume of a sphere of radius 6.

904.78

The work

6.

Find the volume of the ellipsoid
.

959.12

The work

7.

Find the volume of the solid enclosed by the paraboloids and .

3.142

The work

8.

A cylindrical drill with radius 2 is used to bore a hole throught the center of
a sphere of radius 5. Find the volume of the ring shaped solid that
remains.

403.104

The work

9.

A sprinkler distributes water in a circular pattern, supplying water to a depth
of feet per hour at a distance of r feet from the sprinkler.

A. What is the total amount of water supplied per hour inside of a circle of
radius 14?

B. What is the total amount of water that goes throught the sprinkler per hour?

A) 6.2831
B) 6.2831

The work

10.

A volcano fills the volume between the graphs z = 0 and
, and outside the
cylinder . Find the volume of this volcano.

0.1257

The work

11.

A. Using polar coordinates, evaluate the improper integral .