Consider the region bounded on the right by and on the left by for

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

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}

(b)

\dfrac{1}{10}

(c)

\dfrac{1}{30}

(d)

\dfrac{1}{5}