Q. 24.4( 198 Votes )

# 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.

Answer :

Radius (*r*1) of 1st sphere = 6 cm

Radius (*r*2) of 2nd sphere = 8 cm

Radius (*r*3) 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

[r1^{3} + r2^{3} + r3^{3}] = r^{3}

[6^{3} + 8^{3} + 10^{3}] = r^{3}

r^{3} = 216 + 512 + 1000

r^{3} = 1728

r = 12 cm

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

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