Question

How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimension
6cm $\times$ 42 cm $\times$ 21 cm .

Answer 1

The dimensions of the solid rectangular lead piece is $66\mathrm{cm}\times 42\mathrm{cm}\times 21\mathrm{cm}$.
Diameter of the spherical lead shots = 4.2 cm
Let n spherical lead shots be obtained from the rectangular piece.
$$\begin{gathered} n\times \mathrm{volume}\mathrm{of}\mathrm{spherical}\mathrm{lead}\mathrm{shot}=\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{rectangular}\mathrm{lead}\mathrm{piece} \\ \Rightarrow \frac{\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{rectangular}\mathrm{lead}\mathrm{piece}}{\mathrm{volume}\mathrm{of}\mathrm{spherical}\mathrm{lead}\mathrm{shot}}=n \\ \mathit{\Rightarrow }\frac{66\times 42\times 21}{{\displaystyle \frac{4}{3}}{\mathit{\pi r}}^{\mathit{3}}}\mathit{=}n \\ \mathit{\Rightarrow }\frac{66\times 42\times 21}{{\displaystyle \frac{\mathrm{4}}{\mathrm{3}}\pi {\left(\frac{\mathrm{4}\mathrm{.}\mathrm{2}}{\mathrm{2}}\right)}^3}}\mathit{=}n \\ \mathit{\Rightarrow }\frac{58212}{38.808}\mathit{=}n \\ \mathit{\Rightarrow }n\mathit{=}1500 \end{gathered}$$
Hence, 1500 lead shots can be formed.

DISCLAIMER: There is some error in the question given. Instead of 6 cm, there should be 66 cm.
The result obtained is by taking 66 cm as the dimensions of the rectangular piece.