For 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

For

k>0

let

R

be the region bounded by the

x

-axis and the graph of

y=k\sin x

for

0\le x\le\pi

. A solid has base

R

and cross sections perpendicular to the

x

-axis that are semicircles whose diameters lie in

R

. If the volume of the solid is

\pi

, what is the value of

k

? (a)

\dfrac{2}{\sqrt\pi}

(b)

\dfrac{4}{\sqrt\pi}

(c)

\dfrac{2\sqrt2}{\sqrt\pi}

(d)

\dfrac{4}{\pi}