How do I find the total surface area of a cylinder? What is the formula and why?
I always forget whether to use 2pirh or 2pir(h+r). Can someone explain the formula from first principles so I can derive it instead of memorizing?
1 Answer
RJRahul Joshi
✓ Accepted
· 15d ago
▲ 11
A cylinder has 3 surfaces: 2 circular ends + 1 curved surface. Each circular end: area = pir^2. Two ends: 2pir^2. Curved surface: imagine cutting and unrolling it — it becomes a rectangle with width = height of cylinder (h) and length = circumference (2pir). Curved surface area = 2pirh. Total surface area = 2pir^2 + 2pirh = 2pir(r+h). So both expressions are the same! 2pirh is curved surface area only. 2pir(r+h) is the TOTAL surface area. Use 2pir*h when the problem asks for lateral or curved surface area.
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