Three solid glass balls of radii ‘r’ cm, 6 cm and 8 cm are melted into a solid sphere of radius 9 cm. Find the value of ‘r’.

1 cm

Given that the radii of three solid glass balls is ‘r’ cm, 6 cm and 8 cm, sum of the volumes of the three balls

$=\frac{4}{3}πr^3+\frac{4}{3}π(6)^3+\frac{4}{3}π(8)^3$

$=\frac{4}{3}π(r^3+6^3+8^3)cm^3$

The volume of the solid sphere of radius 9 cm

$=\frac{4}{3}π(9)^3=243×4π$

$∴243×4π=\frac{4}{3}π(r^3+728)$ ⇒ r = 1