The ratio of the weights of two spheres is 81 : 64 and the ratio of their weights per cc of material is 3 : 1. The ratio of their radius is?

3 : 4

Weight of sphere = volume × weight per cc

⇒ Volume           :  r³  :   R³

⇒ Weight per cc :  3     :   1   

⇒ Weight           :  81  :  64 

ATQ,

⇒ r³ : R³ = \(\frac{81}{3}\) : 64  =  27  :  64

Hence, r : R = 3 : 4