A solid has base on the -axis for

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

A solid

S

has base on the

x

-axis for

0\le x\le5

. Cross sections perpendicular to the

x

-axis are semicircles whose diameters are

d(x)>0

. A new solid

T

is formed by doubling every diameter value so that each new diameter is

2d(x)

on the same interval. Which of the following describes how the volume of

T

compares to the volume of

S

? (a) The volume of

T

is four times the volume of

S

. (b) The volume of

T

is twice the volume of

S

. (c) The volume of

T

8

times the volume of

S

. (d) The volume of

T

\pi

times the volume of

S