Mathematics

Mathematics

Problem

The region bounded by the parabola

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)

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