Question

A cone of height 20 cm and radius of base 5 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere. 

Answer 1

We have,

the base radius of the cone, r=5 cm and 

the height of the cone, h = 20 cm

Let the radius of the sphere be R.

As,

Volume of sphere = Volume of cone 

`rArr 4/3piR^3 = 1/3pir^2h`

`rArr R^3 = (pir^2hxx3)/(3xx4pi)`

`rArr R^3 = (r^2h)/4`

`rArr R^3 = (5xx5xx20)/4`

`rArr R^3 = 125`

`rArr R = root(3)(125)`

⇒ Diameter of the sphere = 2R= 2×5 = 10 cm

So, the diameter of the sphere is 10 cm.