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Surface Area of a Cylinder
Geometry • Grades 7, 8, 9, 10
Geometry
Surface Area of a Cylinder
Find the total surface area and lateral curved area of a cylinder with A = 2πrh + 2πr².
The Formula
A = 2πrh + 2πr²
Used for: Finding the total surface area (lateral area + 2 circular bases) of a cylinder
ATotal surface area (square units)
rRadius of base
hHeight of cylinder
LLateral area: 2πrh
⚡Live Interactive Quick Solver
Instant CalculationTotal Surface Area (A):471.24 units²
Exact: 150π• Lateral: 314.16 + Bases: 157.08
A = 2\pi rh + 2\pi r^2 = 2\pi r(h + r)
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🎯 Key Concepts & Rules
Essential principles for calculating with this formula:
🥫
Lateral Curved Area = 2πrhUnrolling the side of a cylinder forms a rectangle of width 2πr and height h.
⭕
2 Circular Bases = 2πr²Top and bottom lids each have area πr².
📐
Total Area = 2πr(h + r)Factored formula for fast calculation.
📝 Worked Examples & Step-by-Step Solutions
Example 1: Total Surface Area
Problem:
Cylinder radius r = 3 cm, height h = 7 cm.1
Formula
A = 2πrh + 2πr²2
Lateral Area
2 × π × 3 × 7 = 42π ≈ 131.95 cm²3
Bases Area
2 × π × (3)² = 18π ≈ 56.55 cm²4
Total Sum
A = 42π + 18π = 60π ≈ 188.50 cm²Answer: A = 60π cm² ≈ 188.50 cm²
💡 Pro Tips & Common Mistakes
Open Cylinder (Pipe)
If the ends are open, surface area is just the lateral area: A = 2πrh.
One Lid (Cup)
For an open cup, area is A = 2πrh + πr².
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