Question

Try solving it if you can it’s hard

Answer 1

Ratio of the volumes of two spheres = 64 : 27
Sum of the radii = 21 cm
Let the radius of one of the spheres be 'r' cm
Radius of the other sphere = (21 - r) cm
Ratio of volumes = 4 3 πr3 : 4 3 π(21 - r)3
                         = r3 : (21 - r)3
       r3 : (21 - r)3  =   64 : 27
   ⇒ r3 : (21 - r)3  = 43 : 33
   ⇒ r : (21 - r) = 4 : 3
   ⇒ r (21 - r) = 4 3 
   ⇒ 84 - 4r = 3r
   ⇒ r = 12
Therefore, radius of one of the spheres is 12 cm and the radius of the other sphere is (21 - 12) i.e. 9 cm.