If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere, then the diameter of the new sphere will be :

Solution(By Examveda Team)

Given radii of three metallic spheres be $${r_1},\,{r_2},\,{r_3}$$   are 6 cm, 8 cm and 10 cm respectively
Let the radius of the new sphere be R
$$\eqalign{ & \frac{4}{3}\pi {R^3} = \frac{4}{3}\pi \left( {r_1^3 + r_2^3 + r_3^3} \right) \cr & \Rightarrow \frac{4}{3}\pi {R^3} = \frac{4}{3}\pi \left( {{6^3} + {8^3} + {{10}^3}} \right) \cr & \Rightarrow {R^3} = \left( {216 + 512 + 1000} \right) \cr & \Rightarrow {R^3} = 1728 \cr & \Rightarrow R = \root 3 \of {12 \times 12 \times 12} \cr & \Rightarrow R = 12 \cr} $$
∴ Diameter = 24 cm