Question

How many spherical bullets can be made out of a solid cube of lead whose edge measures $\mathbf{44}\mathbf{}\mathbf{cm}$, each bullet being $\mathbf{4}\mathbf{}\mathbf{cm}$ in diameter ?

Answer 1

Step 1: Given information.

Edge of a solid cube $\left(a\right)=44\mathrm{cm}$

The diameter of each bullet $\left(d\right)=4\mathrm{cm}$

Step 2: Calculate the number of bullets.

Let us consider that $n$ number of bullets is made from the solid cube and the radius of each spherical bullet be $r\mathrm{cm}$.

The radius of each bullet, $r=\frac{4}{2}=2\mathrm{cm}$

So, the volume of the solid cube will be equal to the volume of $n$ number of bullets.

$$\begin{gathered} \therefore \mathrm{Volume}\mathrm{of}\mathrm{solid}\mathrm{cube}=\mathrm{Volume}\mathrm{of}n\mathrm{number}\mathrm{of}\mathrm{bullets} \\ \Rightarrow a^3=n\times \frac{4}{3}\mathrm{\pi }{r}^3 \\ \Rightarrow {\left(44\right)}^3=n\times \left(\frac{4}{3}\times \frac{22}{7}\times 2^3\right) \\ \Rightarrow 85184=n\times \frac{704}{21} \\ \Rightarrow n=85184\times \frac{21}{704} \\ \Rightarrow n=121\times 21 \\ \Rightarrow n=2541 \end{gathered}$$

Hence, $2541$bullets can be made out of the solid cube.