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8.The lateral surface area of a hollow cylinder is 4224 \(cm^2\). It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of the rectangular sheet.
Answer :

Given, The lateral surface area of a hollow cylinder is 4224 \(cm^2\) and the width of rectangular sheet =33cm
We know that the circumference of the base of the cylinder is equal to the length of the sheet and the height of the cylinder is equal to the breadth of the sheet when a hollow cylinder is cut and a rectangular sheet is formed. Therefore, the lateral surface area of the cylinder is equal to the area of the rectangular sheet.

Let the length of the sheet be l.

∴ we have ,area of the sheet = Lateral surface area of cylinder

\(\Rightarrow l \times 33 = 4224\)

\(\Rightarrow l=\frac{4224}{33}=128cm\)

Thus, the length of the rectangular sheet=128cm\)

Now, perimeter of rectangular sheet= 2 (l + b)

\( = 2 (128 + 33) cm\)

\(= 2 \times 161 cm=322 cm\)

Hence, the perimeter of the rectangular sheet=322cm.