Let be the region bounded by the -axis and the graph of for

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

Problem

Let

R

be the region bounded by the

x

-axis and the graph of

y=3-\dfrac{x}{2}

for

0\le x\le6

. Two solids are built on

R

with cross sections taken perpendicular to the

x

-axis. • In Solid M, each cross section is a square whose side length equals the value of

y

at that

x

. • In Solid N, each cross section is a semicircle whose diameter equals the value of

y

at that

x

. What is the value of

\dfrac{V_{M}}{V_{N}}\,?

(a)

\dfrac{4}{\pi}

(b)

\dfrac{8}{\pi}

(c)

\dfrac{\pi}{8}

(d)

\dfrac{2}{\pi}