from a handpicked tutor in LIVE 1-to-1 classes

# 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, the sphere formed by recasting these three spheres will have the same volume equal to the sum of the volumes of the three 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, r₁ = 6 cm

Radius of 2^{nd} sphere, r₂ = 8 cm

Radius of 3^{rd} sphere, r₃ = 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 πr₁^{3} + 4/3 πr₂^{3} + 4/3 πr₃^{3}

r^{3} = [r₁^{3} + r₂^{3} + r₃^{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.

**☛ Check: **NCERT Solutions Class 10 Maths Chapter 13

**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

**Summary:**

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

**☛ Related Questions:**

- A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.
- A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
- A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
- How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?

visual curriculum