Cone Formulas
3D Solids
Cone
- Volume
- V = (1 ⁄ 3) πr2h
- Slant height
- l = √(r2 + h2)
- Curved surface area
- CSA = πrl
- Total surface area
- TSA = πr(r + l)
- r radius
- h height
- l slant height
Cone formulas explained
A right circular cone tapers from a circular base to an apex. Its slant height l comes from the Pythagorean theorem. Below are all the cone formulas with what each letter means, a worked example and a free calculator.
- Volume:
V = (1 ⁄ 3) πr²h - Slant height:
l = √(r² + h²) - Curved surface area:
CSA = πrl - Total surface area:
TSA = πr(r + l)
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Cone calculator
Worked example: volume of a cone
Given Radius r = 3 cm, Height h = 4 cm, substitute the values into each cone formula:
- V = (1 ⁄ 3) × π × 3² × 4 = 37.7 cm³
- l = √(3² + 4²) = 5 cm
- CSA = π × 3 × l = 47.12 cm²
- TSA = π × 3 × (3 + l) = 75.4 cm²
Cone Formula SheetFormulas, variables, a worked example and practice questions with answers.Download PDFOpen
Cone formulas FAQ
What is the formula for the volume of a cone?
The volume of a cone is V = (1 ⁄ 3) πr²h, where r is the radius, h is the height.
What is the formula for the slant height of a cone?
The slant height of a cone is l = √(r² + h²), where r is the radius, h is the height, l is the slant height.
What is the formula for the curved surface area of a cone?
The curved surface area of a cone is CSA = πrl, where r is the radius, l is the slant height.
Can I download the cone formulas as a PDF?
Yes. Use the Download PDF button on this page for a free printable cone formula sheet with a worked example and practice questions.