Mathematics

Problem

The region in the first quadrant bounded by the curves

y = 2x

and

y = x^{2}

is revolved about the

x

-axis to generate a solid. What is the exact volume of this solid? a)

\dfrac{16\pi}{15}

\dfrac{64\pi}{15}

\dfrac{32\pi}{15}

\dfrac{4\pi}{3}