How many coins $ 1.75 \mathrm{~cm} $ in diameter and $ 2 \mathrm{~mm} $ thick must be melted to form a cuboid $ 11 \mathrm{~cm} \times 10 \mathrm{~cm} \times 7 \mathrm{~cm} ? $

Given:

Diameter of each coin $=1.75\ cm$

Thickness of each coin $=2\ mm$

Dimensions of the cuboid are \( 11 \mathrm{~cm} \times 10 \mathrm{~cm} \times 7 \mathrm{~cm} \).

To do:

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

Solution:

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

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

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

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

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

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

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 $=11 \times 10 \times 7$

$=770 \mathrm{~cm}^{3}$

Therefore,

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

$=\frac{\frac{770}{77}}{160}$

$=\frac{770 \times 160}{77}$

$=10 \times 160$

$=1600$

The number of coins that must be melted to form the cuboid is $1600$.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

43 Views

Kickstart Your Career

Get certified by completing the course

Get Started