Let . The region in the first quadrant bounded by , , and is revolved about the…

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

Problem

Let

a>0

. The region in the first quadrant bounded by

x=y^{2}

y=0

, and

y=a

is revolved about the

y

-axis. If the resulting solid has volume

\dfrac{243\pi}{5}

cubic units, what is the value of

a

? (a)

\displaystyle\left(\dfrac{729}{5}\right)^{1/3}

(b)

\displaystyle\left(\dfrac{243}{2}\right)^{1/5}

(c)

3

(d)

\displaystyle\left(\dfrac{3}{5}\right)^{1/5}