Mathematics

Mathematics

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}

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