Question #150546
The surface area of a sphere inscribed in a regular tetrahedron is 144pi cm^2.
1. What is the radius of the sphere?

2. What is the altitude of the tetrahedron?
1
Expert's answer
2020-12-15T02:28:30-0500

The surface area of a sphere inscribed in a regular tetrahedron is 144π cm2144\pi\space cm^2

1. What is the radius of the sphere?

Surface area of a sphere S=4πr2S=4\pi r^2

rr- radius of sphere

r=S4π=144π4π=36=6.r=\sqrt{\frac{S}{4\pi}}=\sqrt{\frac{144\pi}{4\pi}}=\sqrt{36}=6.

Answer: radius of the sphere is 6 cm.6\space cm.

2. What is the altitude of the tetrahedron?

For a regular tetrahedron of edge length a:

Altitude h=23ah=\sqrt{\frac{2}{3}}a

a=2r6=126a=2r\sqrt{6}=12\sqrt{6}

h=23126=24.h=\sqrt{\frac{2}{3}}12\sqrt{6}=24.

Answer:altitude of the tetrahedron is 24 cm.24\space cm.




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