Cone Volume Calculator
Compute the volume of a right circular cone from its radius and height, plus slant height and surface area.
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Input
Enter the base radius and height to compute a right circular cone volume, slant height, lateral area and surface area.
Result
Volume
56.548668
Slant height
6.708204
Lateral area
63.223333
Surface area
91.497666
Use the same length unit for all inputs. Volume is in cubic units and areas in square units.
How it works
- The volume is V = one third times pi times radius squared times height.
- The slant height l is found with l = square root of radius squared plus height squared.
- Lateral area is pi times radius times slant height, base area is pi times radius squared, and surface area is their sum.
- Enter the radius and height in the same length unit. Volume uses cubic units and areas use square units.
- Pi is taken as about 3.14159 in the calculation.
Frequently asked questions
- How is the volume of a cone calculated?
- Use V = 1/3 × π × radius² × height. This is exactly one third of a cylinder (πr²h) that shares the same base and height.
- Why is a cone's volume one third of a cylinder's?
- For a cylinder with the same base radius r and height h, the volume is πr²h, and a cone holds one third of that. The leading 1/3 in the formula captures this relationship.
- Can it also give the slant height and surface area?
- Yes. The slant height is l = √(radius² + height²), the lateral area is π × radius × slant height, the base area is π × radius², and the total surface area is their sum.
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