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?

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