Question

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

Answer 1

Calculate the volume of cylinder

Given data,

Radius (r) of silver coin $=\frac{\mathrm{Diameter}}{2}=\frac{1.75}{2}cm=\frac{17.5}{2}mm$

Thickness (h) of silver coin $=2mm$

Dimensions of cuboid $=5.5cm\times 10cm\times 3.5cm=55mm\times 100mm\times 35mm$

Let $a$ be the number of coins.

$a\times$ volume of $1$ coin $=$ Volume of a box

$$\begin{gathered} \Rightarrow a\times \pi r^{2}h=l\times b\times h \\ \Rightarrow a=\frac{l\times b\times h}{\pi r^{2}h} \end{gathered}$$

Now, substitute the values in the formula, we get

$a=\frac{(55\times 100\times 35\times 2\times 2\times 7)}{(22\times 17.5\times 17.5\times 2)}$

On solving,

$a=400$

Therefore, the number of silver coins that have to be melted are $400$.