Question

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

Answer 1

coin 1.75 cm diametor $r=\frac{1.75}{2}$

thick = 2 mm = 0.2 cm

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

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

$=0.153\pi .c{m}^3$

$\to$ volume of cuboid $=11\times 10\times 7$

$=770c{m}^3$

$\to$ volume of cuboid = $noofcoins\times volumeofcoin$

$\therefore 770=n\times 0.153\pi$

$\therefore n=\frac{770}{0.153\times \pi }=1600.$