Mathematics

Problem

Let

R

be the region bounded by

x=y^{2}

and

x=6-y^{2}

. Cross sections perpendicular to the

y

–axis are semicircles. What is the volume of the resulting solid? a)

\dfrac{48\pi\sqrt{3}}{5}

\dfrac{24\pi\sqrt{3}}{5}

\dfrac{12\pi\sqrt{3}}{5}

\dfrac{96\pi\sqrt{3}}{5}