Mathematics

Problem

A region is bounded by the curve

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

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

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

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