The surface area of a sphere inscribed in a regular tetrahedron is 144π cm2
1. What is the radius of the sphere?
Surface area of a sphere S=4πr2
r− radius of sphere
r=4πS=4π144π=36=6.
Answer: radius of the sphere is 6 cm.
2. What is the altitude of the tetrahedron?
For a regular tetrahedron of edge length a:
Altitude h=32a
a=2r6=126
h=32126=24.
Answer:altitude of the tetrahedron is 24 cm.
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