Mathematics

Problem

The region between the curve

y=x^{2}

and the line

y=4

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

x

-axis are semicircles whose diameters lie in the region. What is the volume of the solid? a)

\dfrac{128\pi}{15}

\dfrac{32\pi}{15}

\dfrac{64\pi}{15}

\dfrac{256\pi}{15}