Answer to Question #150531 in Geometry for Louise Lane Romualdo

Question

The surface area of a sphere inscribed in a regular tetrahedron is 144 cm2
What is the radius of the sphere?

Answer 1

The surface area of the sphere od radius $r$ is

$$S=4\pi r^2$$

Then

$$r=\sqrt{\dfrac{S}{4\pi}}$$

Given $S=144\ cm^2$

$$r=\sqrt{\dfrac{144 \ cm^2}{4\pi}}=\dfrac{6\sqrt{\pi}}{\pi} \ cm$$

$$r=\dfrac{6\sqrt{\pi}}{\pi} \ cm\approx3.385\ cm$$