# Ex.11.3 Q8 Mensuration Solution - NCERT Maths Class 8

## Question

The lateral surface area of a hollow cylinder is \(4224\, \rm{cm^2}\) .It is cut along its height and formed a rectangular sheet of width \(33\,\rm{ cm.}\) Find the perimeter of rectangular sheet?

## Text Solution

**What is Known?**

A hollow cylinder is cut along its height to from a rectangular sheet. The lateral surface of the cylinder is given.

**What is unknown?**

Perimeter of the rectangular sheet.

**Reasoning:**

The length of rectangular sheet will be equal to the circumference of the circle. Lateral surface area of the cylinder will be equal to the area of rectangular sheet.

**Steps:**

Lateral surface area of a hollow cylinder \(=4224\,\rm{m^2}\)

Width of rectangular sheet \(= 33\,\rm{cm}\)

Let length of the rectangular sheet \(=l\)

Area of cylinder = Area of rectangular sheet

\[\begin{align}4224\,\rm{m^2} &= 33 \rm{cm} \times l\\l &= \frac{{4224}}{{33}}\,\rm{cm}\\&= 128\,\rm{cm} \end{align}\]

Thus, the length of the rectangular sheet is \(128 \,\rm{cm.}\)

Perimeter of the rectangular sheet

\[\begin{align} &=2 \times ({\rm{length}} \times {\rm{width}})\\&= 2 \times (128\,{\rm{cm}} \times 33\,{\rm{cm}})\\&= 2 \times 161\,{\rm{cm}}\\&= 322\,{\rm{cm}}\end{align}\]

Thus, the perimeter of rectangular sheet is \(322\,\rm{ cm.}\)