Let be the solid generated when the region bounded by the curve and the -axis on is…

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

Problem

Let

S

be the solid generated when the region bounded by the curve

y=2x-x^{2}

and the

x

-axis on

0\le x\le2

is revolved about the horizontal line

y=3

. Which of the following is the volume of

S

? (a)

\displaystyle \frac{136\pi}{15}

(b)

\displaystyle \frac{52\pi}{15}

(c)

\displaystyle \frac{104\pi}{15}

(d)

\displaystyle \frac{208\pi}{15}