Mathematics

Problem

Let

R

be the region bounded by the

x

–axis and the graph of

y=\sin x

for

0\le x\le\pi

. Two solids are built on

R

with cross sections perpendicular to the

x

–axis. • In Solid

A

the cross sections are squares. • In Solid

B

the cross sections are rectangles whose height is twice their base width lying in

R

. Compute the ratio

\dfrac{V_{B}}{V_{A}}

of the volumes of the two solids.