How do I find a cone's volume?
One third of pi times radius squared times height. A cone holds exactly a third of the cylinder that would fit around it with the same base and height.
// maths › 3D Solids
Cone Volume Calculator
Find a right circular cone's volume, total surface area and slant height from its base radius and vertical height.
volume = ⅓πr²h ; slant = √(r²+h²) ; surface = πr(r+slant)
Frequently asked questions
What is the slant height?
The distance from the base edge up to the tip, along the sloping surface. It is the square root of radius squared plus height squared, by Pythagoras.
Why is the volume only a third of a cylinder?
It is a geometric fact, provable with calculus or by filling: three identical cones exactly fill their matching cylinder. The factor of one third is exact.
What is the surface area of a cone?
The base circle plus the curved surface: pi r times (r + slant height). Leave out the base if the cone is open, like an ice-cream cone.
Where is this used?
Ice-cream cones, funnels, party hats, piles of sand or grain, and the pointed tops of towers and roofs.