# 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:**

A figure is drawn below to visualize the shapes.

As three metallic spheres are melted and recast into a single solid sphere then the sphere formed by recasting these spheres will be the same in volume as the sum of the volumes of spheres.

Volume of the resulting sphere = Sum of the volumes of three spheres.

We will find the volume of the sphere by using formula;

Volume of the sphere = 4/3πr^{3}

where r is the radius of the sphere

Radius of 1^{st} sphere, r_{1} = 6 cm

Radius of 2^{nd} sphere, r_{2} = 8 cm

Radius of 3^{rd} sphere, r_{3} = 10 cm

Let the radius of the resulting sphere be r.

Volume of the resulting sphere = Sum of the volumes of three spheres

4/3 πr^{3} = 4/3 πr_{1}^{3} + 4/3 πr_{2}^{3} + 4/3 πr_{3}^{3}

r^{3} = [r_{1}^{3} + r_{2}^{3} + r_{3}^{3}]

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

r^{3} = [216 cm^{3} + 512 cm^{3} + 1000 cm^{3}]

r^{3} = 1728 cm^{3}

r = 12 cm

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

**Video 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

### NCERT Solutions for Class 10 Maths - Chapter 13 Exercise 13.3 Question 2:

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

The radius of the single solid sphere resulting from melting three metallic spheres of radii 6 cm, 8 cm, and 10 cm is 12 cm