Answer to Question #150234 in Geometry for solid mensuration

Question #150234
The surface area of a sphere inscribed in a regular tetrahedron is 144 cm2
21. What is the radius of the sphere?

a) 12 cm
b) 7 cm
c) 6 cm
d) 5 cm
1
Expert's answer
2020-12-17T05:59:25-0500


Let "a=" base of a regular tetrahedron, "l=" slant height of a a regular tetrahedron, "r=" radius of a sphere inscribed in a regular tetrahedron.

The surface area of a sphere


"A=4\\pi r^2"

Given "A=144cm^2"

"4\\pi r^2=144""r^2=\\dfrac{36}{\\pi}"

"r=\\dfrac{6\\sqrt{\\pi}}{\\pi}\\approx3.4(cm)"

No correct answer.



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