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

Question

asked Jun 9, 2021 105k views

1 Answer

Afforess · Answer 1 · 2021-06-15T05:20:01+0000

Answer:

$144\pi in^2$

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