Question

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

Answer 1

Coins are cylindrical in shape as shown in the figure.
Given:
Height ($h_1$) of cylindrical coins $=2mm$ $=0.2cm$

Radius ($r$) of circular end of coins = $\frac{1.75}{2}=0.875cm$

Let $x$ coins be melted to form the required cuboid.

Volume of cylinder = $\pi r^{2}h$

Volume of a cuboid = $l\times b\times h$
When a solid is converted from one form to another, the amount of volume remains the same

Volume of $x$ cylindrical coins = Volume of cuboid

$\Rightarrow$$x\times \pi r^2{h}_1=l\times b\times h$

$\Rightarrow x\times \pi \times {0.875}^2\times 0.2=5.5\times 10\times 3.5$

$\Rightarrow x=\frac{5.5\times 10\times 3.5\times 7}{{0.875}^2\times 0.2\times 22}=400$

So, the number of coins melted to form such a cuboid is $400$.