Cylinder Curved Surface Area

Quick answer: For a right circular cylinder, curved surface area is 2πrh. Unrolling its curved side gives a rectangle of width 2πr and height h. Total area of a closed cylinder is 2πrh + 2πr².

Worked example

Find curved and total surface area when r = 3 cm and h = 10 cm.

1. Curved area = 2π×3×10 = 60π cm².
2. Each circular end has area π×3² = 9π cm².
3. Two ends contribute 18π cm².
4. Closed total area = 60π + 18π = 78π cm².

Check the result

The unrolled side is 6π cm by 10 cm, whose area is 60π cm².

Common mistake to avoid

If diameter is given, halve it first. A cylinder open at one end has only one circular base in its surface area.

Try it yourself

1. Find curved area for diameter 8 cm and height 5 cm. 2. Find total area for the same cylinder open at one end.

Answers and reasoning

1. r = 4: curved area = 40π cm². 2. Add one base 16π, giving 56π cm².

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