A student states that for the region bounded by ( )

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

Problem

A student states that for the region bounded by

y=cx

(

c>0

), the

x

-axis, and the lines

x=0

and

x=3

, the volume produced by revolving the region about the

x

-axis will double whenever

c

is doubled. Which of the following best evaluates this claim? (a) The claim is true; the volume is proportional to

c

, so doubling

c

doubles the volume. (b) The claim is false; the volume is proportional to

c^{3}

, so doubling

c

multiplies the volume by

8

.},{ (c) The claim is false; the volume is proportional to

c^{2}

, so doubling

c

multiplies the volume by

4

.},{ (d) The claim cannot be evaluated without additional information about the constant

c

and its units.