Question

A metal parallelopiped of measures 16 cm $\times$11 cm $\times$10 cm was melted to make coins. How many coins were made if the thickness and diameter of each coin was 2 mm and 2 cm respectively ?

Answer 1

Radius of each coin, r = $\frac{2}{2}$ = 1 cm

Thickness of each coin, h = 2 mm = $\frac{2}{10}$ = 0.2 cm (1 cm = 10 mm)

Let the number of coins made be n.

It is given that a metal parallelopiped is melted to make the coins.

∴ n × Volume of metal in each coin = Volume of the metal parallelopiped

$$\begin{gathered} \Rightarrow n=\frac{\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{metal}\mathrm{parallelopiped}}{\mathrm{Volume}\mathrm{of}\mathrm{metal}\mathrm{in}\mathrm{each}\mathrm{coin}} \\ \Rightarrow n=\frac{16\times 11\times 10}{\mathrm{\pi }{r}^{2}h} \\ \Rightarrow n=\frac{16\times 11\times 10}{{\displaystyle \frac{22}{7}}\times {\left(1\right)}^2\times 0.2}=2800 \end{gathered}$$
Thus, the number of coins made are 2800.