Mathematics

Problem

Region

R

consists of two subregions: • For

0\le y\le1

, the region is bounded by

x=y^2

and the

y

-axis. • For

1\le y\le2

, the region is bounded by

x=y

and the

y

-axis. The entire region

R

is revolved about the

y

-axis. What is the volume of the solid generated? a)

\dfrac{32\pi}{15}

\dfrac{40\pi}{15}

\dfrac{38\pi}{15}

\dfrac{35\pi}{15}