Answer to Question #150749 in Geometry for solid mensuration

Question

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

Answer 1

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 $A=144cm^2$

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

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

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