Question

The lateral surface area of a hollow cylinder is 4356cm square. It is cut height and formed a rectangular sheet of width 33cm. Find the perimeter of rectangular sheet?

Answer 1

Given data : The lateral surface area of a hollow cylinder is 4356 cm². It is cut along its height and formed a rectangular sheet of width 33 cm.

To find : Find the perimeter of rectangular sheet?

Solution : Here, a/c to question;

➜ Area of sheet = 4356 cm²

➜ Width/breadth of sheet = 33 cm

Here, a/c to question;

Now, by formula of area of rectangle;

➜ Area of sheet = Length * Breadth

➜ 4356 = Length * 33

➜ Length = 4356/33

➜ Length = 132 cm

Now, by formula of perimeter of the rectangle;

➜ Perimeter of sheet = 2 * {Length + Breadth}

➜ Perimeter of sheet = 2 * {132 + 33}

➜ Perimeter of sheet = 2 * 165

➜ Perimeter of sheet = 330 cm

Answer : Hence, the perimeter of the rectangular sheet is 330 cm.

{Alternative method :

➜ Lateral surface area = 2πrh

Where, h = 33 cm {a/c to given data}

➜ 4356 = 2 * 22/7 * r * 33

➜ 4356 = 44/7 * 33 * r

➜ 4356 = 1452/7 * r

➜ r = {4356/1452} * 7

➜ r = 3 * 7

➜ r = 21 cm

Here, we know that, perimeter of circle is equal to length of the sheet {a/c to given data}

➜ Length of sheet = 2πr

➜ Length of sheet = 2 * 22/7 * 21

➜ Length of sheet = 2 * 22 * 3

➜ Length of sheet = 44 * 3

➜ Length of sheet = 132 cm

Here, we know that, length and breadth of sheet are 132 cm and 33 cm respectively.

Now,

Now, by formula of perimeter of the rectangle;

➜ Perimeter of sheet = 2 * {Length + Breadth}

➜ Perimeter of sheet = 2 * {132 + 33}

➜ Perimeter of sheet = 2 * 165

➜ Perimeter of sheet = 330 cm}