Question

A sphere and a cube have same surface area. Find the ratio of their volumes.

Answer 1

SA of a sphere: 4πr² 
SA of a cube: 6x² 

4πr² = 6x² 
r²/x² = 6 / 4π 
(r/x)² = 3 / 2π 
r/x = (3 / 2π)^0.5 

Volume of a sphere: 4/3 πr³ 
Volume of a cube: x³ 
Find the ratio meaning (4/3 πr³)/x³ 
= (4π/3)(r³/x³) 
= (4π/3)(r/x)³ 
= (4π/3)(3 / 2π)^1.5 
= (2²π/3)[3^1.5 / (2^1.5)(π^1.5)] 
= √2√3 / √π 
= √(6/π) 
≈1.38