A solid is formed by revolving a planar region about the -axis

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

A solid

S

is formed by revolving a planar region about the

x

-axis. For

0 \le x \le 1

each cross section perpendicular to the

x

-axis has outer radius

3

and inner radius

x

. For

1 \le x \le 2

the outer radius is

4

while the inner radius remains

x

. Calculate the exact volume of

S