Radius (r1) of 1st sphere = 6 cm

Radius (r2) of 2nd sphere = 8 cm

Radius (r3) of 3rd 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

[r1³ + r2³ + r3³] = r³

[6³ + 8³ + 10³] = r³

r³ = 216 + 512 + 1000

r = 1728

r = 12 cm

Hence, the radius of the resulting sphere, r = 12 cm