Question

Choose the correct answer of the following question:

The number of solid spheres, each of diameter 6 cm, that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm, is

(a) 2 (b) 4 (c) 5 (d) 6 [CBSE 2014]

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{spher},r=\frac{6}{2}=3\mathrm{cm}, \\ \mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{cylinder},H=45\mathrm{cm}\mathrm{and} \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{cylinder},R=\frac{4}{2}=2\mathrm{cm} \\ \mathrm{Now}, \\ \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{sphere}\mathrm{that}\mathrm{can}\mathrm{be}\mathrm{made}=\frac{\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cylinder}}{\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{sphere}} \\ =\frac{\mathrm{\pi }{R}^{2}H}{\left({\displaystyle \frac{4}{3}}\mathrm{\pi }{r}^3\right)} \\ =\frac{3R^{2}H}{{\displaystyle 4r^3}} \\ =\frac{3\times 2\times 2\times 45}{{\displaystyle 4\times 3\times 3\times 3}} \\ =5 \end{gathered}$$

Hence, the correct answer is option (c).