Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and
lines about the x-axis.
-$$y = \sqrt { x } , y = 0 , y = x - 6$$
A) $27 \pi$
B) $\frac { 63 } { 4 } \pi$
C) $\frac { 225 } { 2 } \pi$
D) $\frac { 63 } { 2 } \pi$

Question

Quizplus · Accepted Answer

The shell method involves integrating the product of the circumference of the shell, the height of the shell, and the thickness of the shell. The region is bounded by $y = \sqrt{x}$, $y = 0$, and $y = x - 6$. The intersection points are $x = 0$ and $x = 9$. The volume is calculated by integrating $2\pi y (x_2 - x_1)$ from $y = 0$ to $y = 3$, resulting in $\frac{63}{2} \pi$.

Use the Shell Method to Find the Volume of the Solid