How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions $5.5\ cm \times 10\ cm \times 3.5\ cm$?

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Given:

Diameter of each coin $=1.75\ cm$

The thickness of each coin $=2\ mm$

Dimensions of the cuboid are $5.5 \mathrm{~cm} \times 10 \mathrm{~cm} \times 3.5 \mathrm{~cm}$.

To do:

We have to find the number of coins that must be melted to form the cuboid.

Solution:

Radius of the coin $r=\frac{1.75}{2}$

$=\frac{175}{100 \times 2}$

$=\frac{7}{8} \mathrm{~cm}$

The thickness of the coin $h=2 \mathrm{~mm}$

$=\frac{2}{10} \mathrm{~cm}$

$=\frac{1}{5} \mathrm{~cm}$

The volume of each coin $=\pi r^{2} h$

$=\frac{22}{7} \times (\frac{7}{8})^{2} \times \frac{1}{5}$

$=\frac{22}{7} \times \frac{7}{8} \times \frac{7}{8} \times \frac{1}{5}$

$=\frac{77}{160} \mathrm{~cm}^{3}$

Volume of the cuboid $=5.5 \times 10 \times 3.5$

$=192.5 \mathrm{~cm}^{3}$

Therefore,

Number of coins formed $=$ Volume of the cuboid $\div$ Volume of each coin

$=\frac{\frac{192.5}{77}}{160}$

$=\frac{192.5 \times 160}{77}$

$=2.5 \times 160$

$=400$

The number of coins that must be melted to form the cuboid is $400$.

Updated on 10-Oct-2022 13:25:34