An iron spherical ball has been melted and recast into smaller balls of equal size. If the radius of each of the smaller balls is 1/4 of the radius of the original ball, how many such balls are made? Compare the surface area, of all the smaller balls combined together with that of the original ball.

Let the radius of bigger spherical be R


Volume of bigger spherical ball = 3


Radius of smaller spherical ballR


Volume of smaller ball 3


Let number of equal size spherical balls be n


Volume of n equal spherical ball =Volume of bigger spherical ball



⇒ n × (R/4)3 R3


⇒ n = 43


⇒ n = 64 balls


Surface area of bigger spherical ball =4π R2


Surface area of smaller spherical ball 2


Ratio between the surface area of bigger and 64 smaller spherical ball



30