Question

The region enclosed by the semicircle is revolved completely around the x-axis. A. Describe the solid of revolution that is formed b. Find its volume in terms of pi.

Answer 1

The volume of this sphere =
`(4)/(3)* \pi r^(3)`

Explanation:

The region enclosed by the semicircle is revolved completely around the x-axis . Then the solid formed is a sphere of the same radius as that of the semicircle. We have to find the volume of this sphere. If the semicircle had center at the origin then the sphere also has the center at the origin.

Let the radius of given circle = r

Surface area of this sphere =
`4\pi r^(2)`

The volume of this sphere =
`(4)/(3)\pi* r^(3)`

This is the volume of the required solid.