Question

Find, in terms of π, the surface area of a sphere generated by rotating a semicircle of radius 6 inches about its diameter.

Answer 1

`144\pi in^2`

Explanation:

Given

Shape: Circe

Radius = 6 inches

Required

What is the surface area of a sphere when the circle

When a circle is rotated about its diameter, the resulting sphere maintains the same radius and diameter as the circle, before rotation;

This implies that

Radius [of sphere] = 6 inches

`Surfare\ Area = 4\pi r^2`

Substitute 6 for r

`Surfare\ Area = 4\pi* 6^2`

`Surfare\ Area = 4\pi* 6 * 6`

`Surfare\ Area = 4\pi*36`

`Surfare\ Area = 144\pi`

Hence, the surface area of the resulting sphere is 144 pi inches square