#### Question

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.

#### Solution

Radius (*r*_{1}) of 1^{st} sphere = 6 cm

Radius (*r*_{2}) of 2^{nd} sphere = 8 cm

Radius (*r*_{3}) of 3^{rd} 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

`4/3pi[r_1^3+r_2^3+r_3^3] = 4/3pir^3`

`4/3pi[6^3+8^3+10^3] = 4/3 pir^3`

r^{3} = 216 + 512 + 1000 = 1728

r = 12 cm

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

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Solution 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. Concept: Conversion of Solid from One Shape to Another.