Question

The total volume of two spheres is 10π cubic units. The ratio of the

areas is 4:9. What is the volume of the smaller sphere in cubic units?

Answer 1

4 r1 ² π : 4 r2² π = 4 : 9
r1² : r2² = 4 : 9
r1 : r2 = 2 : 3
r2 = 3 r1/2   ( r - radius of the smaller sphere )
10 π = 4/3 r³ π + 4/3 ( 3 r/2 ) ³ π    /  : π/3
30 = 4 r³  + 4 * 27 r³/8
30 = 4 r³ + 27 r³/2    / * 2
60 = 35 r³
r³ = 60 / 35 = 12/7
V ( Smaller ) = 4/3 r³ π = 4/3 * 12 / 7 π = 16/7 π = 2.286 π cubic units