The curved surface area of a cylinder is calculated using the formula: 2πrh, where 'r' is the radius and 'h' is the height of the cylinder.
Here's a breakdown of how to use this formula:
Understanding the Formula
- 2πr: This part of the formula calculates the circumference of the circular base of the cylinder. Remember that π (pi) is approximately 3.14159.
- h: This represents the height of the cylinder.
Multiplying the circumference of the base by the height gives you the area of the curved surface, as if you were "unrolling" the cylinder's side into a rectangle.
Steps to Calculate the Curved Surface Area
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Determine the radius (r) of the cylinder's base. If you are given the diameter, divide it by 2 to find the radius.
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Determine the height (h) of the cylinder.
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Apply the formula: Curved Surface Area = 2πrh
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Substitute the values of r and h into the formula.
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Calculate the result. You can use a calculator to find the value of 2πrh.
Example
Let's say you have a cylinder with:
- Radius (r) = 5 cm
- Height (h) = 10 cm
Then, the curved surface area would be:
Curved Surface Area = 2 π 5 cm 10 cm
Curved Surface Area = 2 3.14159 5 cm 10 cm
Curved Surface Area ≈ 314.16 cm²
Therefore, the curved surface area of this cylinder is approximately 314.16 square centimeters.
Key Points
- Make sure the units for the radius and height are the same before calculating the area. If they are different, convert one of them.
- The curved surface area only includes the area of the side of the cylinder. It does not include the area of the top and bottom circular bases. To find the total surface area, you would also need to calculate the area of those circles (2 * πr²) and add it to the curved surface area.
