Question

Choose the correct answer of the following question:

A metallic solid sphere of radius 9 cm is melted to form a solid cylinder of radius 9 cm. The height of the cylinder is

(a) 12 cm (b) 18 cm (c) 36 cm (d) 96 cm [CBSE 2014]

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{solid}\mathrm{sphere},R=9\mathrm{cm}\mathrm{and} \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{solid}\mathrm{cylinder},r=9\mathrm{cm} \\ \mathrm{Let}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{cylinder}\mathrm{be}h. \\ \mathrm{Now}, \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cylinder}=\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{sphere} \\ \Rightarrow \mathrm{\pi }{r}^{2}h=\frac{4}{3}\mathrm{\pi }{R}^3 \\ \Rightarrow h=\frac{4R^3}{3r^2} \\ \Rightarrow h=\frac{4\times 9\times 9\times 9}{3\times 9\times 9} \\ \therefore h=12\mathrm{cm} \end{gathered}$$

Hence, the correct answer is option (a).