Question

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.

Answer 1

Let the radius of the big ball be x cm

The, the radius of the small ball = x/4 cm

And, let the number of balls = n

Then according to the question, we have

Volume of n small balls = Volume of the big ball

n x 4/3 π(x/4)³ = 4/3 πx³

n x (x³/ 64) = x³

n = 64

Therefore, the number of small balls = 64

Next,

Surface area of all small balls/ surface area of big ball = 64 x 4π(x/4)²/ 4π(x)²

= 64/16 = 4/1

Thus, the ratio of the surface area of the small balls to that of the original ball is 4:1