Question

Find the number of coins, $1.5$ cm in diameter and $0.2$ cm thick, to be melted to form a right circular cylinder of height 10 cm and diameter $4.5$ cm.

Answer 1

volume of each coin $=\pi r^{2}h=\pi {\left(\frac{1.5}{2}\right)}^2\times \left(0.2\right)$

$=\frac{\pi }{4}\left(2.25\right)\left(0.2\right)$

$Volumeofeachcoin=\frac{\pi }{4}\times \left(0.45\right)c{m}^2$

Volume of cylinder to be formed $=\pi R^{2}H$

$=\pi {\left(\frac{4.5}{2}\right)}^2\times 10$

$=\frac{\pi }{4}\left(20.25\right)\times 10$

$Volumeofcylindertobeformed=\frac{202.5\pi }{4}c{m}^3$

$noofcoinstobeneeded=\frac{volumeofcylindertobeformed}{volumeofeachcoin}$

$=\frac{\frac{\pi }{4}\times \left(202.5\right)}{\frac{\pi }{4}\times \left(0.45\right)}$

$=\frac{20250}{45}$

$no.ofcoinsneeded=450$

$\therefore$ we need to melt $450$ coins to form the required cylinder.