Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.

Given: Radius (r1) of first sphere = 6 cm
Radius (r2) of second sphere = 8 cm
Radius (r3) of third sphere = 10 cm
Radius of the resulting sphere = r

The object formed by recasting these spheres will be the same in volume as the sum of the volumes of these spheres.
So, Volume of 3 spheres = Volume of resulting sphere
(4/3)π[r1³ + r2³ + r3³] = (4/3)πr³
=> (4/3)π[6³ + 8³ + 10³] = (4/3)πr³
=> 216 + 512 + 1000 = r³
=> 1728 = r³
r = 12 cm

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