A solid lead 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 sphere can be made of ?

166

We know that,

Volume of a sphere = \(\frac{4}{3}\)πr³

We have,

Radius of solid sphere = 11 cm

Radius of small solid sphere = 2 cm 

Volume of the solid sphere with radius 11 cm = \(\frac{4}{3}\)× π × 11³

Volume of the small solid sphere with radius 2 cm = \(\frac{4}{3}\)× π × 2³

Number of small solid sphere = \(\frac{4}{3}\)× π × 11³ $\div$   \(\frac{4}{3}\) × π × 2³ = \(\frac{1331}{8}\) = 166