Question

A spherical steel ball is melted to make a 8new identical balls find the ratio of the radius of the each new ball to radius of the original ball

Answer 1

Let the radius of the spherical steel ball be 'X'
Then the volume of the spherical steel ball=4/3πr³=4/3π(X)³
Let the radius of the small spherical balls be 'x'
Then, Volume=4/3π(x)³
According to question:-
4/3π(X)³=8[4/3πx³]
4/3(X)³=32/3x³
(X)³=8x³
X=2x
Therefore ratio- 1:2

Answer 2

let the radius of original ball be : R 
let the radius of new ball be r.
Volume of the original ball is equal to the total volume of 8 new balls.
4/3 * π R³ = 8 * 4/3 * π r³

=>    R = 2 r  
=>    Ratio:   r : R = 1 : 2