Mathematics

Problem

For

k>4

, let

T(k)

denote the solid obtained by revolving the region bounded by the curve

y=4-x^{2}

, the

x

-axis, and the lines

x=-2

and

x=2

about the horizontal line

y=k

. Which of the following gives

T(k)

’s volume as a function of

k

? a)

\displaystyle V(k)=\frac{32\pi\,(5k-8)}{15}

\displaystyle V(k)=32\pi\,(k-2)

\displaystyle V(k)=\frac{64\pi\,(5k-8)}{15}

\displaystyle V(k)=\frac{64\pi\,(5k+8)}{15}