Cone Volume Calculator
Enter the radius of the base and the vertical height of the cone to get its volume, slant height and surface area.
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Formula
- Volume:
V = π × r² × h ÷ 3 - Slant height:
l = √(r² + h²) - Total surface area:
A = π × r × (r + l)
Worked example
Radius 3 and height 4: l = √(9 + 16) = 5, V = π × 9 × 4 ÷ 3 = 12π ≈ 37.6991 and A = π × 3 × (3 + 5) = 24π ≈ 75.3982.
Frequently asked questions
What is the formula for the volume of a cone?
V = π × r² × h ÷ 3, one third of the cylinder with the same base and height. With radius 3 and height 4, V = 12π, about 37.6991.
How do I find the slant height?
Use the Pythagorean theorem: slant = √(r² + h²). For radius 3 and height 4 that is √25 = 5.
How is the surface area of a cone calculated?
A = π × r × (r + slant height): the curved side π × r × slant plus the circular base π × r². With radius 3 and slant 5, A = 3π × 8 = 24π, about 75.3982.
Is the height the same as the slant height?
No. The height is measured straight down from the tip to the centre of the base. The slant height runs along the side, so it is always longer.