Mathematics

Problem

A solid has base in the region bounded by the graphs of

y=x

and the

x

-axis for

0\le x\le 4

. Cross sections perpendicular to the

x

-axis are semicircles with diameters that span from the

x

-axis up to the curve

y=x

. Determine the volume of the solid. a)

\dfrac{16\pi}{3}

\dfrac{8\pi}{3}

\dfrac{4\pi}{3}

\dfrac{32\pi}{3}