# How many coins 1.75 cm in diameter and 2 mm

Question:

How many coins 1.75 cm in diameter and 2 mm thick must be melted to form a cuboid 11 cm × 10 cm × 7 cm?

Solution:

The dimension of the cuboid is 11cm10cm7cm. Therefore, the volume of the cuboid is

$V_{1}=11 \times 10 \times 7=770 \mathrm{~cm}^{3}$

The radius and thickness of each coin are $\frac{1.75}{2}=0.875 \mathrm{~cm}$ and $2 \mathrm{~mm}=0.2 \mathrm{~cm}$ respectively. Therefore, the volume of each coin is

$V_{2}=\pi \times(0.875)^{2} \times 0.2 \mathrm{~cm}^{3}$

Since, the total volume of the melted coins is same as the volume of the cuboid; the number of required coins is

$\frac{V_{1}}{V_{2}}=\frac{770}{\pi \times(0.875)^{2} \times 0.2}$

$=\frac{770 \times 7}{22 \times(0.875)^{2} \times 0.2}$

$=1600$