Question

Three solid metallic balls of radii 3 cm, 4 cm and 5 cm are melted and moulded into a single solid ball. The radius of the new ball is :

Answer 1

volume of the moulded ball = sum of the volumes of three balls

let the radii of three balls r1, r2, r3 respectively and of the moulded ball R

since the balls are spherical therefore there volume will be =4/3 pi r^3

according to question

4/3 pi R^3 = 4/3 pi (r1^3+r2^3+r3^3)

4/3 pi will be cancelled

R^3=27+64+125

R= cube root of 216

6cm

hence the radius of the resulting ball is 6cm