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 the same in volume as the sum of the volumes of these spheres.
The volume of 3 spheres = Volume of resulting sphere
[r13 + r23 + r33] = r3
[63 + 83 + 103] = r3
r3 = 216 + 512 + 1000
r3 = 1728
r = 12 cm
Hence, the radius of the resulting sphere, r = 12 cm.
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