Question

The radius of a solid sphere is 3 cm. It is melted and recasted into smaller spheres with diameter 0.6 cm. Find the number of spheres recasted.

Answer 1

Given :

Radius of solid sphere (R) 3 cm

Diameter of the sphere recasted = 0.6 cm

its radius = \(\frac { 0.6 }{ 2 }\) =0.3 cm

Volume of solid sphere = \(\frac { 4 }{ 3 }\)π(0.3)³ cm³

Volume of sphere recated = \(\frac { 4 }{ 3 }\)π(0.3)³ cm³

Let the number spheres recasted be n.

∴ Volume of solid sphere n × volume of sphere recasted

Volume of solid sphere n × volume of sphere recasted.

n = \(\frac { 3\times 3\times 3 }{ 0.3\times 0.3\times 0.3 } \)

= 1000

Hence the number of spheres reasted = 1000