Mathematics

Problem

Let

R

be the region in the

xy

-plane bounded above by

y=4

and below by

y=x^{2}

. A solid is constructed so that for

-2\le x\le2

, the cross sections perpendicular to the

x

-axis are rectangles whose height is twice the base width. What is the volume of the solid? a)

\dfrac{512}{15}

\dfrac{1024}{15}

\dfrac{256}{15}

\dfrac{2048}{15}