Question

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

Answer 1

Given that radius of each of smaller ball = 1/4 Radius of original ball.

Let radius of smaller ball be r.

Radius of ** ball be 4r

Curved surface area of sphere = 4r2

Surface area of big ball ( S1) = 4π(4r)2 ....…(3)

Surface area of each small ball ( S2) = 4πr2

Total surface area of 64 small *****

Therefore, Total surface area of small ***** is equal to 4 times surface area of big ball.