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Question

An iron spherical ball of radius 21 cm is melted and it is re-cast into small hemispheres radius 7 cm each. The number of hemispheres formed will be


  1. 54

  2. 52

  3. 48

  4. 50


Solution

The correct option is A

54


Given,

Radius of the spherical ball,R=21 cm

Radius of each hemispherical ball,r=7 cm

The volume will remain constant as same volume of iron metal is used to re-cast the hemispherical balls.

Let's assume x such hemispherical balls will be formed.

So, Volume of spherical ball = x × Volume of each hemispheical ball 

43πR3=x×23πr3
43×π×213=x×23×π×73

x=54

After re-casting 54 small hemispherical balls are formed.

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