Question

Find the number of solid spheres, each of diameter 6 cm, that could be moulded to form a solid metallic cylinder of height 45 cm and diameter 4 cm.

Answer 1

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

So, the number of solid spheres so moulded is 5.