   Chapter 5.3, Problem 11E

Chapter
Section
Textbook Problem

# Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. y = x 3 / 2 ,    y = 8 ,    x = 0

To determine

To find:

The volume generated by rotating the region bounded by the given curves about the x-axis using the cylindrical shells.

Explanation

1) Concept:

i. If y  is the radius of the typical shell, then the circumference =2πy .

ii. By the shell method the volume of the solid by rotating the region under the curve y=f(x) about the x- axis from a to b is

V= ab2πyf(y)dy

where  0ab

2) Given:

The region bounded by y=x32, x=0, y=8 rotated about the x- axis.

3) Calculation:

As the region is bounded by

y=x32 x=y23, x=0, y=8

Using the shell method, find the typical approximating shell with the radius y

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