Page 83 - Calc for the Clueless

Again, h is small.

Example 6—

Find the volume if our region is rotated about the y axis.

As you rotate this region there is a hole. The outside radius is always 9 and the inside radius is always the x
2
4
2
value. But x = y . r = x = y .
2

Example 7—

Find the volume of our glorious region if it is rotated about the line x = 9.

Notice that when we rotate the region about x = 9, there is no hole. V sect = πr h. r = 9 - x = 9 - y r = 81 - 18y +
2 2
2
2
y . h = ∆y.
4