Use cylindrical shells to find the volume of the solid when the region enclosed by x = y², x = 0, y = 3 is revolved about the x-axis. A) 13.5 $\pi$ B) 40.5 C) 81 $\pi$ D) 40.5 $\pi$ E) ( $\pi$)

Question

Quizplus · Accepted Answer

The volume of the solid can be found using the method of cylindrical shells. The formula for the volume using cylindrical shells is V = ∫[a to b] 2π(radius)(height) dy. Here, the radius is y, and the height is y^2. The limits of integration are from y = 0 to y = 3. Thus, V = ∫[0 to 3] 2π(y)(y^2) dy = 2π∫[0 to 3] y^3 dy = 2π[y^4/4] from 0 to 3 = 2π(81/4) = 40.5π.

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

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