MATH 2210 12.4 Double Integrals using Polar Coordinates
Solutions to selected homework problems
Problem 29: Let the top of the pool lie in the xy plane and let the shallow end correspond
to x = -20 and the deep end be x = 20. The slope of the bottom of the pool is
8
1
40
5
so the equation of the bottom is
2
9
8
1 xz
and the region of integration is the circle
222
20 yx
. Using polar coordinates, the volume is given by
3
2
0
2
0
2
0
20
0
20
0
23
2
0
20
0
2
0
20
0
ft1800
900sin
3
1000
900cos
3
1000
4
9
cos
24
1
2
9
cos
8
1
2
9
8
1
0
d
drr
ddrrr
xzddrrzV
