+1234 A sphere is inscribed in a cone with height $3$ and base radius $3$. What is the ratio of the volume of the sphere to the volume of the cone?
+129883 
Note that triangle ADO is similar to triangle AEC
AO / DO = AC / EC
AO = 3 - r
DO = r
AC = sqrt [ 3^2 + 3^2 ] = 3sqrt [2]
EC = 3
(3 - r) / r = 3sqrt (2 ) / 3
3 - r = r *sqrt (2)
3 = r [ 1 + sqrt 2]
r = 3 / [1 + sqrt 2] ≈ 1.24
Volume of sphere = (4/3)(pi)(1.24)^3 ≈ 2.54 pi = A
Volume of cone = (1/3) pi (3^2) * 3 = 9pi = B
A / B ≈ 2.54 / 9 = 127 / 450
