Question

How many lead shots, each 3 mm in diameter, can be made from a cuboid with dimensions (12 cm × 11 cm × 9 cm)?

Answer 1

Here, l = 12 cm, b = 11 cm and h = 9 cm

$$\begin{gathered} \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cuboid}=l\times b\times h \\ =12\times 11\times 9 \\ =1188{\mathrm{cm}}^3 \end{gathered}$$

Radius of one lead shot = 3 mm= $\frac{0.3}{2}\mathrm{cm}$

$$\begin{gathered} \mathrm{Volume}\mathrm{of}\mathrm{one}\mathrm{lead}\mathrm{shot}=\frac{4}{3}\times \frac{22}{7}\times {\left(\frac{0.3}{2}\right)}^3 \\ =\frac{11\times 9}{7000} \\ =0.014{\mathrm{cm}}^3 \end{gathered}$$

$$\begin{gathered} \therefore \mathrm{Number}\mathrm{of}\mathrm{lead}\mathrm{shots}=\frac{\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{cuboid}}{\mathrm{volume}\mathrm{of}\mathrm{one}\mathrm{lead}\mathrm{shot}} \\ =\frac{1188}{0.014} \\ =84857.14\approx 84857 \end{gathered}$$