Cone Calculator
Enter a radius and height below to instantly get volume, surface area, and slant height.
Cone Formulas
Volume = (1/3)πr²h. Slant height = √(r² + h²). Surface area = πr(r + slant height).
Worked example
A cone with radius 3 and height 4.
Slant height = √(3² + 4²) = √25 = 5
Volume = (1/3) × π × 9 × 4 = 12π ≈ 37.70
Surface area = π × 3 × (3 + 5) = 24π ≈ 75.40
Frequently Asked Questions
What is the formula for the volume of a cone?
Volume = (1/3) × π × r² × h — exactly one third the volume of a cylinder with the same radius and height.
What is slant height, and how is it different from height?
Height is the straight vertical distance from the base to the tip. Slant height is the distance along the cone's outer surface from the edge of the base to the tip, found with the Pythagorean theorem: slant height = √(r² + h²).
What is the formula for the surface area of a cone?
Surface area = πr(r + l), where l is the slant height — this adds the circular base (πr²) to the curved lateral surface (πrl).
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