Cone Calculator
V = ⅓πr²h | SA = πr(r + l) | l = √(r²+h²)
A cone is a 3D shape with a circular base that tapers to a point (apex). It appears in architecture (roofs, towers), nature (pine trees), and everyday objects (ice cream cones, funnels).
- 1Identify radius r (base) and height h (perpendicular from base to apex)
- 2Slant height: l = √(r² + h²)
- 3Volume: V = ⅓πr²h
- 4Lateral (curved) surface area: LA = πrl
- 5Total surface area: SA = πr(r + l)
r=5, h=12=V=314.16, SA=282.74l=√(25+144)=13
r=3, h=4=V=37.70, SA=75.40l=5 (3-4-5 triple)
| Property | Formula |
|---|---|
| Slant height | l = √(r² + h²) |
| Volume | V = ⅓πr²h |
| Lateral area | LA = πrl |
| Total surface area | SA = πr² + πrl = πr(r + l) |
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Fun Fact
The Great Pyramid of Giza would have a volume of about 2.5 million cubic metres if it were a perfect cone — but it's actually a square pyramid, slightly less.
References
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