Question

How many lead shots each 3 mm in diameter can be made from a cuboid of dimensions 9 cm $\times$ 11 cm $\times$ 12 cm?

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Radius}\mathrm{of}\mathrm{a}\mathrm{lead}\mathrm{shot},r=\frac{3}{2}=1.5\mathrm{mm}=0.15\mathrm{cm}\mathrm{and} \\ \mathrm{Dimensions}\mathrm{of}\mathrm{the}\mathrm{cuboid}\mathrm{are}9\mathrm{cm}\times 11\mathrm{cm}\times 12\mathrm{cm} \\ \mathrm{Now}, \\ \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{the}\mathrm{lead}\mathrm{shots}=\frac{\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cuboid}}{\mathrm{Volume}\mathrm{of}\mathrm{a}\mathrm{lead}\mathrm{shot}} \\ =\frac{9\times 11\times 12}{\left({\displaystyle \frac{4}{3}}\mathrm{\pi }{r}^3\right)} \\ =\frac{9\times 11\times 12}{\left({\displaystyle \frac{4}{3}\times \frac{22}{7}\times 0.15\times 0.15\times 0.15}\right)} \\ =84000 \end{gathered}$$

So, the number of lead shots that can be made from the cuboid is 84000.