A region is bounded by the curve

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

Problem

x = \sqrt{y}

, the

y

-axis, and the lines

y=0

and

y=9

. The region is revolved about the

y

-axis to create a solid. Which of the following definite integrals represents the volume of the solid? (a)

\displaystyle \pi\int_{0}^{9} \sqrt{y}\,dy

(b)

\displaystyle 2\pi\int_{0}^{9} y\,dy

(c)

\displaystyle \pi\int_{0}^{9} (\sqrt{y})^{2}\,dy

(d)

\displaystyle \pi\int_{0}^{3} x^{2}\,dx