Question

Two spheres of same metal weight 1kg and 7kg with the smaller sph ...

Answer 1

Ans: Given weight of two spheres of same metal are 1 kg and 7kg and radius of smaller sphere = 3cm

=> Volume of smaller sphere = 4/3 pi (3cm)^3
= 4/3 pi 27 cm^3
= 4 pi x 9cm^3
= 36 pi cm^3

Thus 1 kg occupies 36 pi cm^3 space also when both spheres are melted the weight of re-casted sphere is equal to sum of individual weights of sphere

=> weight of re-casted = 1kg + 7kg = 8kg

Let the radius or re-casted sphere be r. 
Then weight of re-casted sphere occupies volume re-casted sphere space

=> 8kg occupies 4/3 pi r^3 space
=> 8 x 36pi cm^3 = 4/3 pi r^3
=> r^3 = 8x36x3/4 cm^3 = 216 cm^3 = 6cm^3

Hence the required radius of the sphere is 6cm.