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.

Radius of first sphere (r₁) = 6 cm, Radius of second sphere (r₂) = 8 cm
Radius of third sphere (r₃) = 10 cm,
Let the radius of the new sphere = r
According to question, volumes of three spheres = Volume of new sphere
⇒ 4/3π(r₁³ + r₂³ + r₃³) 4/3πr ³ ⇒ 4/3π (6³+ 8³ + 10³) = 4/3πr³
⇒ 216 + 512 + 1000 = r³ ⇒ r³ = 1728 ⇒ r = 12 cm
Hence, the radius of resulting sphere is 12 cm.