Mathematics

Problem

Consider the region bounded on the right by

x=y

and on the left by

x=y^{2}

for

0\le y\le1

. Cross sections perpendicular to the

y

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

\dfrac{3}{10}

\dfrac{1}{10}

\dfrac{1}{30}

\dfrac{1}{5}