The region in the –plane bounded by the –axis and the graph of for is revolved about…

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

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}

(b)

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

(c)

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

(d)

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