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

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## 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 $$322\,\rm{ cm.}$$

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