Question

The lateral surface area of a hollow cylinder is $4224c{m}^2$. It is cut along its height and formed a rectangular sheet of width$33cm$. Find the perimeter of rectangular sheet?

Answer 1

Step 1: Find CSA of hollow cylinder

Let us assume the radius of the cylinder as$r$

Curved surface area of hollow cylinder $=2\pi rh$

$\begin{array}{rcl}4224& =& 2\times \pi \times r\times 33\\ r& =& \frac{\left(4224\right)}{(2\pi \times 33)}\\ r& =& 64\times \frac{7}{22}\end{array}$

Step 2: Find length of rectangular sheet

Length of rectangular sheet, $l=2\pi r$[Since, Length = circumference]

$l=2\times \frac{22}{7}\times (64\times \frac{7}{22})=128$

So the length of the rectangular sheet is$128cm.$

Step 3: Find the perimeter of the rectangular sheet

Also, Perimeter of rectangular sheet$=2\times (l+b)$

$=2\times (128+33)=322cm$

Hence, the perimeter of the rectangular sheet is $322cm.$