Mathematics

Problem

The region in the

xy

–plane bounded by the

x

–axis and the graph of

y=6-x^{2}

for

0\le x\le \sqrt{6}

is revolved about the

x

–axis. What is the exact volume of the resulting solid? a)

\displaystyle \frac{192\pi\sqrt6}{5}

\displaystyle \frac{48\pi\sqrt6}{5}

\displaystyle \frac{96\pi\sqrt6}{5}

\displaystyle \frac{144\pi\sqrt6}{5}