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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 33cm.Find the perimeter of rectangular sheet?
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The lateral surface area of a hollow cylinder is 4224 cm^2.It is cut a...
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The lateral surface area of a hollow cylinder is given as 4224 cm², and the width of the rectangular sheet formed after cutting the cylinder along its height is 33 cm.
Understanding the Lateral Surface Area
The formula for the lateral surface area (LSA) of a cylinder is:
Where:
- r = radius of the cylinder
- h = height of the cylinder
Since the cylinder is cut along its height, the height of the cylinder becomes the length of the rectangular sheet.
Finding the Height of the Cylinder
We know the lateral surface area:
Relating Width and Length of the Sheet
The width of the rectangular sheet is given as 33 cm. When the cylinder is cut, the length of the sheet will be equal to the circumference of the base of the cylinder, which is:
Thus, the length of the rectangular sheet is also 2πr.
Calculating the Perimeter
The perimeter (P) of a rectangle is calculated using the formula:
Substituting the known values:
Final Calculation
To find the perimeter, we need the value of r. However, since we only have the lateral surface area and width, we can express the perimeter in terms of r:
This is the expression for the perimeter of the rectangular sheet formed from the hollow cylinder. The exact value of the perimeter can be calculated once the radius is determined.
The lateral surface area of a hollow cylinder is given as 4224 cm², and the width of the rectangular sheet formed after cutting the cylinder along its height is 33 cm.
Understanding the Lateral Surface Area
The formula for the lateral surface area (LSA) of a cylinder is:
- LSA = 2πrh
Where:
- r = radius of the cylinder
- h = height of the cylinder
Since the cylinder is cut along its height, the height of the cylinder becomes the length of the rectangular sheet.
Finding the Height of the Cylinder
We know the lateral surface area:
- 4224 = 2πrh
- h = 4224 / (2πr)
Relating Width and Length of the Sheet
The width of the rectangular sheet is given as 33 cm. When the cylinder is cut, the length of the sheet will be equal to the circumference of the base of the cylinder, which is:
- Circumference = 2πr
Thus, the length of the rectangular sheet is also 2πr.
Calculating the Perimeter
The perimeter (P) of a rectangle is calculated using the formula:
- P = 2(length + width)
Substituting the known values:
- P = 2(2πr + 33)
Final Calculation
To find the perimeter, we need the value of r. However, since we only have the lateral surface area and width, we can express the perimeter in terms of r:
- P = 4πr + 132
This is the expression for the perimeter of the rectangular sheet formed from the hollow cylinder. The exact value of the perimeter can be calculated once the radius is determined.
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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 33cm.Find the perimeter of rectangular sheet?
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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 33cm.Find the perimeter of rectangular sheet? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about 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 33cm.Find the perimeter of rectangular sheet? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 33cm.Find the perimeter of rectangular sheet?.
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 33cm.Find the perimeter of rectangular sheet? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about 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 33cm.Find the perimeter of rectangular sheet? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 33cm.Find the perimeter of rectangular sheet?.
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