Use cylindrical shells to find the volume of the solid when the region enclosed by xy = 12, x + y = 8 is revolved about the x-axis.
A) 21.332 $\pi$
B) 0.01 $\pi$
C) 10.667 $\pi$
D) ( $\pi$)
E) 21.333 $\pi$

Question

Quizplus · Accepted Answer

The volume of the solid can be found using the method of cylindrical shells. The region is bounded by the curves xy = 12 (a hyperbola) and x + y = 8 (a straight line). When revolved around the x-axis, the volume can be calculated by integrating the surface area of cylindrical shells. The correct calculation leads to the volume being 21.333π, which matches choice E.

Use Cylindrical Shells to Find the Volume of the Solid π\piπ

Use Cylindrical Shells to Find the Volume of the Solid $\pi$