Question

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

Answer 1

Hint-In this particular type of question we have to equate the lateral surface area of the cylinder with the total area of the rectangular sheet and thus find the length of the rectangular sheet . Then we need to apply the formula of perimeter of a rectangle to get to the desired result .

Complete step-by-step answer:
Given that, the hollow cylinder is converted into a rectangular sheet . So the area of the rectangular sheet will be equal to the area of the cylinder .
Curved or lateral surface area of the cylinder = area of the rectangular sheet
We know area of rectangular sheet= $length \times width$
4224 = $length \times width$
$ \Rightarrow $4224 = $length \times 33$ ( since Curved or lateral surface area of the cylinder = 4224$c{m^2}$and width = 33 cm )
$ \Rightarrow length = \dfrac{{4224}}{{33}} = 128cm$
Now the perimeter = $2 \times \left( {length + width} \right)$
$ \Rightarrow perimeter = 2 \times \left( {128 + 33} \right) = 2 \times 161 = 322cm$

Note-Always remember that the lateral surface is the curve part of the cylinder which is made from a rectangular sheet by folding , thus the area of the sheet remains same with the lateral part . Recall the formula of area and perimeter of simple 2D figures like a rectangle to solve such kinds of questions .