Question

How many coins of diameter 1.5 cm and 0.2 cm thickness are formed by melting a right circular cylinder of height 8 cm and diameter 6 cm?

Answer 1

Diameter of the cylinder = 6 cm
$\Rightarrow$ Radius of the cylinder (r) = 3 cm
Height of the cylinder (h) = 8 cm

Volume of the cylinder
$=\pi r^{2}h=\pi \times 3\times 3\times 8c{m}^3$
$=72\pi c{m}^3$

Diameter of the coin = 1.5 cm
$\Rightarrow$ Radius of the coin = $\frac{1.5}{2}$ cm
Height = Thickness of the coin = 0.2 cm

Volume of the each coin
$=\pi {\left(\frac{1.5}{2}\right)}^2\times \left(0.2\right)=\frac{9}{80}\pi c{m}^3$

$\therefore$ Number of coins $=\frac{Volumeofcylinder}{Volumeofacoin}$

$=72\pi ÷\frac{9\pi }{80}=640$