Question

How many solid cylinders of radius 10 cm and height 6 cm can be made by melting a solid sphere of radius 30 cm?

Answer 1

Given:

Radius of a sphere, r = 30 cm

Radius of the cylinder, R = 10 cm

Height of the cylinder, H = 6 cm

Let the number of cylinders be n.

Volume of the sphere = n × Volume of a cylinder

∴ n = `"Volume of the sphere"/"Volume of a cylinder"`

= `(4/3 pi(r)^3)/(pi(R)^2H)`

= `(4/3 xx (30)^3)/(10^2 xx 6)`

= `(4/3 xx 30 xx 30 xx 30)/(10 xx 10 xx 6)`

= 60

∴ 60 cylinders can be made.