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 :

Answer: Option B

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
$$\begin{array}{rl}& \frac{4}{3}\pi R^3=\frac{4}{3}\pi \left(r_1^3+r_2^3+r_3^3\right)\\ & \Rightarrow \frac{4}{3}\pi R^3=\frac{4}{3}\pi \left(6^3+8^3+{10}^3\right)\\ & \Rightarrow R^3=\left(216+512+1000\right)\\ & \Rightarrow R^3=1728\\ & \Rightarrow R=\text{root}3\text{of}12\times 12\times 12\\ & \Rightarrow R=12\end{array}$$
∴ Diameter = 24 cm