Radius (r_{1}) of 1^{st} sphere = 6 cm

Radius (r_{2}) of 2^{nd} sphere = 8 cm

Radius (r_{3}) of 3^{rd} sphere = 10 cm

Let the radius of the resulting sphere be r.

The object formed by recasting these spheres will be same in volume as the sum of the volumes of these spheres.

Volume of 3 spheres = Volume of resulting sphere

Therefore, the radius of the sphere so formed will be 12 cm.