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

Answer: Option B

Volume of new sphere :
$$\begin{array}{rl}& =\left[\frac{4}{3}\pi \times {\left(6\right)}^3+\frac{4}{3}\pi \times {\left(8\right)}^3+\frac{4}{3}\pi \times {\left(10\right)}^3\right]\text{ c}{\text{m}}^3\\ & =\left[\frac{4}{3}\pi \left\{{\left(6\right)}^3+{\left(8\right)}^3+{\left(10\right)}^3\right\}\right]\text{ c}{\text{m}}^3\\ & =\left(\frac{4}{3}\pi \times 1728\right)\text{c}{\text{m}}^3\\ & =\left[\frac{4}{3}\pi \times {\left(12\right)}^3\right]\text{ c}{\text{m}}^3\end{array}$$
Let the radius of the new sphere be R
Then,
$$\begin{array}{rl}& \frac{4}{3}\pi R^3=\frac{4}{3}\pi \times {\left(12\right)}^3\\ & \Rightarrow R=12cm\end{array}$$
∴ Diameter :
$$\begin{array}{rl}& =2R\\ & =2\times 12\\ & =24cm\end{array}$$