The region bounded by and for is revolved about the -axis

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

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}