Curved Surface of a Cylinder
Side (curved) surface area of a cylinder.
Formula
Variables
Example
Radius 2, height 5: curved area = 2π·2·5 ≈ 62.8 square units.
How it works
This formula gives the area of just the curved side of a cylinder, not including the top and bottom circles. It works because if you cut the curved surface and unroll it, it becomes a rectangle with width equal to the circle's circumference, 2πr, and height h. So the area is circumference × height = 2πr × h.
When to use it
Use this when you need the lateral surface area of a cylindrical object, such as a pipe, can, tube, or tank wall. It is useful in packaging, painting, labeling, and material estimation problems.
Worked example, step by step
Find the curved surface area of a cylinder with radius 3 cm and height 10 cm. A = 2πrh A = 2π × 3 × 10 A = 60π A ≈ 188.5 cm² So, the curved surface area is 60π cm², or about 188.5 cm².
Common mistakes to avoid
- Including the top and bottom circle areas instead of only the curved side
- Using the diameter instead of the radius in the formula
- Forgetting to multiply by the height or leaving the answer in linear units instead of square units
Did You Know?
Peel the label off a soup can and it's a rectangle: height by circumference.
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