Question

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

Answer 1

Step 1: Compute the volume of Coin

Given,

Diameter of coin$=1.75cm$

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

Height $h=2mm$

$=0.2cm$

$\therefore$Volume of coin $V=\pi r^{2}h$

$=\mathrm{\pi }\times {\left(\frac{1.75}{2}\right)}^2\times 0.2$

Step 2: Calculate the number of coins

Given, the dimensions of the cuboid are $11cm\times 10cm\times 7cm$.

$\therefore$Volume of cuboid$=11cm\times 10cm\times 7cm$

$=770c{m}^3$

$\therefore$Volume of $n$ coins = volume of cuboid.

$\Rightarrow$$n\times \mathrm{\pi }\times {\left(\frac{1.75}{2}\right)}^2\times 0.2=770$

$\Rightarrow$ $n=\frac{770\times 4\times 10\times 7}{22\times 2\times 1.{75}^2}$

$=\frac{215600}{134.75}$

$=1600$

Hence, the number of coins to be melted to form a cuboid is $1600$.