Mathematics

Problem

A solid has base the region under the parabola

y=4-x^{2}

and above the

x

–axis. Cross sections perpendicular to the

x

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

\dfrac{32\pi}{15}

\dfrac{256\pi}{15}

\dfrac{64\pi}{15}

\dfrac{128\pi}{15}