# An iron spherical ball has been melted and recast into smaller balls of equal size.

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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.

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

Let radius of smaller ball be r.

Radius of bigger 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 balls

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