Mathematics

Problem

Let R be the region in the xy-plane bounded by the curves

x=y^{2}

and

x=4

for

0\le y\le 2

. A solid S is formed by taking R as its base and erecting square cross sections perpendicular to the y-axis. Determine the volume of S. a)

\displaystyle\frac{16}{3}

\displaystyle\frac{512}{15}

\displaystyle\frac{256}{15}

\displaystyle\frac{64}{3}