The region bounded by the parabola

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

Problem

y=x^{2}

, the

x

-axis, and the vertical lines

x=0

and

x=2

is revolved about the horizontal line

y=k

, where

k>4

. Which of the following gives the volume

V(k)

of the resulting solid? (a)

\pi\left(\dfrac{16k}{3}+\dfrac{32}{5}\right)

(b)

\pi\left(\dfrac{16k}{3}-\dfrac{32}{5}\right)

(c)

\pi\left(2k^{2}-\dfrac{16k}{3}+\dfrac{32}{5}\right)

(d)

\pi\left(2k^{2}-\dfrac{8k}{3}+\dfrac{32}{5}\right)