# A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

**Solution:**

A figure is drawn to visualize the shapes according to the given question.

As a metallic sphere is melted and recast into the shape of a cylinder, their volume must be the same.

Volume of the sphere = Volume of the cylinder

Let us find the volume of the sphere and cylinder by using formulae;

Volume of the sphere = 4/3πr^{3} where r is the radius of the sphere

Volume of the cylinder = πr^{2}h where r and h are radius and height of the cylinder respectively

Radius of the sphere, r₁ = 4.2 cm

Radius of the cylinder, r₂ = 6 cm

Let the height of the cylinder be h.

Volume of sphere = Volume of cylinder

4/3πr₁^{3} = πr₂^{2}h

(4/3)r₁^{3} = r₂^{2}h

h = 4r₁^{3} / 3r₂^{2}

= (4 × 4.2 cm × 4.2 cm × 4.2 cm) / (3 × 6 cm × 6 cm)

= 2.744 cm

Hence, the height of the cylinder so formed will be 2.744 cm.

**Video Solution:**

## A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

### NCERT Solutions for Class 10 Maths - Chapter 13 Exercise 13.3 Question 1 :

**Summary:**

If a metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm, the height of the cylinder is 2.744 cm.