Cone Surface Area Calculator
SA = πr² + πrl, where l = √(r² + h²) is the slant height.
Result
Surface area (with base)
174.0299
Lateral 123.76 + base 50.27.
- Radius4
- Height9
- Slant height9.848858
- Lateral surfaceπr × slant123.764397
- Base circleπr²50.265482
- Total SA (closed)174.029880
- Open SA (no base)123.764397
- Volume150.796447
Step-by-step
- Slant height = √(r² + h²) = √(4² + 9²) = 9.8489.
- Lateral surface = πr × slant = 123.7644.
- Base = πr² = 50.2655.
- Total = 174.0299.
How to use this calculator
- Enter base radius and height.
- Read SA (with or without base).
About this calculator
A cone's surface has two parts: lateral (curved side) and base (circle). Lateral surface = πr × slant, where slant = √(r² + h²). Total SA = πr² + πr × slant = πr(r + slant). Many real cones are open (party hats, ice cream cones) — use just the lateral. The lateral, when unrolled, is a circular sector of radius = slant, arc-length = circumference of base = 2πr.
Frequently asked
The lateral surface, when flattened, is a circle sector with radius = slant and arc length = 2πr (the cone's base circumference).
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