Cone Volume & Surface Area Calculator
Full cone calculator: volume, lateral area, total surface area, and slant height from radius and height.
Volume
150.7964
Lateral Sa123.7644
Total Sa174.0299
Slant Height9.8489
Formule
## Cone Formulas ### Volume **V = (1/3) × pi × r² × h** ### Slant Height **l = sqrt(r² + h²)** ### Surface Area - **Lateral area** = pi × r × l - **Total area** = pi × r × l + pi × r² = pi × r × (l + r)
Exemple Résolu
Cone with radius 4 and height 9.
- 01Slant = √(16+81) = √97 ≈ 9.8489
- 02Volume = (1/3)×pi×16×9 = 48pi ≈ 150.7964
- 03Lateral SA = pi×4×9.8489 ≈ 123.7168
- 04Total SA = 123.7168 + pi×16 ≈ 173.9460
Questions Fréquentes
How is a cone related to a cylinder?
A cone with the same base and height as a cylinder has exactly 1/3 the volume of that cylinder.
What is the slant height?
The slant height is the distance from the apex (tip) to any point on the base circle, measured along the surface. It is found using the Pythagorean theorem.
What is a truncated cone (frustum)?
A frustum is a cone with the top cut off by a plane parallel to the base. Its volume requires both radii and the height.
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