Question

A spherical ball of radius 3 cm is melted and recast into three spherical balls.The radius of the two of the balls are 1.5 cm and 2 cm respectively. Determine the diameter of the third ball.

Answer 1

$\to$ As total volume would

remain constant,

$\frac{4}{3}\pi r^3=\frac{4}{3}\pi r_1^3.+\frac{4}{3}\pi r_2^3+\frac{4}{3}\pi r_3^3$

$\Rightarrow r^3=r_1^3+r_2^3+r_3^3$

$\Rightarrow 3^3={1.5}^3+2^3+r_3^3$

$\Rightarrow 27=\frac{27}{8}+8+r_3^3$

$\Rightarrow r_3^3=19-\frac{27}{8}=\frac{125}{8}$

$\Rightarrow r_3=\frac{5}{2}\Rightarrow$ diameter $=5cm$