Question

How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm .

Answer 1

Diameter of the spherical lead shots = 4 cm
Edge length of the solid cube (a) = 44 cm.
Let n be the number of spherical lead shots made out of the solid cube.
$$\begin{gathered} n\times Volumeofthesphericalleadshots=Volumeofthesolidcube \\ \Rightarrow \frac{Volumeofthesolidcube}{Volumeofthesphericalleadshots}=n \\ \Rightarrow \frac{a^3}{{\displaystyle \frac{4}{3}}{\mathrm{\pi r}}^3}=n \\ \Rightarrow \frac{{44}^3}{\frac{4}{3}\mathrm{\pi }\times {\left({\displaystyle \frac{4}{2}}\right)}^3}=n \\ \Rightarrow 2541=n \end{gathered}$$
Hence, 2541 spherical lead shots can be made