Question

A large sphere of radius 14 cm is melted and recast into smaller spheres of radius 3.5 cm. Find the number of smaller spheres that can be made?
1. 100
2. 64
3. 81
4. 27

Answer 1

Correct Answer - Option 2 : 64

Given:

Radius of bigger sphere(R) = 14 cm

Radius of smaller sphere(r) = 3.5 cm

Concept:

Since, the bigger sphere is melted and recast into smaller spheres, their volume will remain same.

Formula used:

Volume of sphere = (4/3) πr³

Calculation:

Let, ‘n’ number of smaller spheres be formed.

Volume of bigger sphere = n × (volume of 1 small sphere)

⇒ (4/3) πR³ = n × (4/3) πr³

⇒ (14)³ = n × (3.5)³

⇒ n = (14 × 14 × 14)/(3.5 × 3.5 × 3.5)

⇒ n = 64

∴ The number of smaller spheres is 64.