A cube of maximum possible volume is cut from a sphere of radius 5√3 cm. What is the ratio of the volume of a cube to that of the sphere?
Diagonal of cube = Diameter of sphere √3 a = 2 (5√3) a = 10 cm Required ratio = volume of cube: volume of sphere = (10)³: 4/3π (5√3)³ = 1000: 4/3 π × 25 × 3 √3 = 2:√3π
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