Mathematics

Problem

The region between the curves

x=y

and

x=2y

for

0\le y\le 3

is the base of a solid. Cross sections perpendicular to the

y

–axis are semicircles. Which definite integral represents the volume

V

of the solid? a)

V=\displaystyle\int_{0}^{3}\frac{\pi}{2}y^{2}\,dy

V=\displaystyle\int_{0}^{3}\frac{\pi}{4}y^{2}\,dy

V=\displaystyle\int_{0}^{3}\frac{\pi}{8}y^{2}\,dy

V=\displaystyle\int_{0}^{3}\pi y^{2}\,dy