The lateral surface area of a hollow cylinder is 4224 cm2. It is cut along its height and formed a rectangular sheet of width 33 cm. find the perimeter of rectangular sheet.
Answers
Answer:
- Perimeter of rectangular sheet is 322 cm.
Step-by-step explanation:
Given
- L.S.A of a hollow cylinder = 4224 cm²
Cylinder is formed into a rectangular sheet :
- Rectangular sheet width = 33 cm
To find
- Perimeter of rectangular sheet
Solution
It is given that a cylinder is converted to rectangle, that means the area of both cylinder and rectangle will be the same. According to the question, the curved/lateral surface area of cylinder is equal to the area of rectangle.
- 4224 = Length × Breadth/Width
- 4224 = Length × 33
- Length = 4224/33
- Length = 128
Hence, the length of rectangular sheet is 128 cm.
Perimeter of rectangular sheet will be :
- 2 (Length + Breadth)
- 2(128 + 33)
- 2(161)
- 322
Hence, the perimeter of rectangular sheet is 322 cm.
Heya ,
Good question !!!!
What we need to do :
As it is given that it is cut along its height and formed a rectangular sheet so we will find height with the help of the lateral surface area of hollow cylinder .
After finding height , its given to find perimeter of sheet which is rectangular so we will simply find it by putting the formula . Then , all set
Solution
4224 = 48 × h
h = 4224 / 48 ( dividing )
h = 88
Perimeter of rectangular sheet = 2 × (l + b)
= 2× (88 + 48)
= 2 × 136
= 272 cm
Hence , The perimeter of rectangular sheet is 272 cm .