Let be the region bounded by and

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

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}

(b)

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

(c)

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

(d)

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