Question

What is the least number of solid metallic spheres, each of 6 cm diameter, that should be melted and recast to form a solid metal cone whose height is 45 cm and diameter 12 cm?

Answer 1

Let the number of solid metallic spheres be 'n'

Volume of 1 sphere 

= `4/3pi(3)^3` 

Volume of metallic cone 

= `1/3pi6^2 xx 45` 

`n = "Volume of metal cone"/"Volume of 1 sphere"` 

`=> n = (1/3pi6^2 xx 45)/(4/3pi(3)^3)` 

`=> n = (6 xx 6 xx 45)/(4 xx 3 xx 3 xx 3)` 

`=>` n = 15 

The least number of spheres needed to form the cone is 15