Mathematics

Mathematics

Problem

The region bounded by

y = ax

and

y = x^{2}

for

x \ge 0

is revolved about the

x

-axis, where

a > 0

is chosen so that the curves intersect only at

(0,0)

and

(a,a^{2})

. If the volume of the resulting solid is

\dfrac{64\pi}{15}

cubic units, what is the value of

a

? a)

\sqrt{2}

b)

2

c)

\sqrt[4]{32}

d)

\left(\dfrac{64}{5}\right)^{1/5}

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