Question

Circular discs 5 mm thickness, are placed one above the other to form a cylinder of curved surface area $462c{m}^2$. Find the number of discs, if the radius of each disc is 3.5 cm.

Answer 1

$\text{Thickness of disc}=5\text{mm}=\frac{5}{10}\text{cm}=0.5\text{cm}$
$\text{Radius of disc}=3.5\text{cm}$
$\text{Curved surface area of the cylinder}=462c{m}^2$
$\text{So,}2\pi rh=462c{m}^2-c{m}^2-\left(i\right)$
$\text{Let the number of discs be x}$
Therefore, height of the cylinder, $h=$ Thickness of disc $\times$ number of discs $=0.5x$
$\text{So,}2\pi rh=2\times \frac{22}{7}\times 3.5\times 0.5x-\left(ii\right)$
From (i) and (ii), we get
$2\times \frac{22}{7}\times 3.5\times 0.5x=462$
$\Rightarrow x=\frac{462\times 7}{2\times 22\times 3.5\times 0.5}=42\text{discs}$