A sphere of radius $4$ inches is inscribed in a cone with a base of radius $8$ inches. In inches, what is the height of the cone? Express your answer as a decimal to the nearest tenth.
A
D
4
E 8 C
triangle ADE similar to triangle AEC
AE / DE = AC / EC
h / 4 = sqrt [h^2 + 8^2] / 8
8h = 4sqrt [ h^2 + 64]
2h = sqrt [ h^2 + 64 ] square both sides
4h^2 = h^2 + 64
3h^2 = 64
h^2 = 64 / 3
h = 8 / sqrt 3 ≈ 4.6
+937 
