Mathematics

Mathematics

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}

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