Question

A solid sphere of radius 11 cm is melted and recast into small solid spheres of radius 2 cm each. How many maximum number (in integer) of such spheres can be made?
1. 125
2. 166
3. 100
4. 30

Answer 1

Correct Answer - Option 2 : 166

Given:

Radius of solid sphere = 11 cm

Radius of small solid sphere = 2 cm 

Formula Used:

Volume of a sphere = (4/3)πr³

Number of small sphere = (Volume of solid sphere)/(Volume of small solid sphere)

Where, r = Radius of the sphere 

Calculation:

Volume of the solid sphere with radius 11 cm = (4/3) × π × 11³

Volume of the small solid sphere with radius 2 cm = (4/3) × π × 2³

Number of small solid sphere = (4/3) × π × 11³/(4/3) × π × 2³ = 1331/8 = 166.37 ≈ 166

∴ Maximum 166 of such spheres can be made.