How it is calculated
A cone has a third of the volume of a cylinder with the same base and height. The slant height is the hypotenuse of a triangle with legs r and h.
V = 1/3 πr²h
Where the numbers come from
- Base radius
- Height
Example
Radius 3, height 4. Slant height 5, volume 1/3 × π × 9 × 4 ≈ 37,7.
Questions
Does it work for a frustum of a cone?
No. A bucket with two radii needs its own formula with r and R.
What is the slant height?
The line from the apex to the base edge along the cone’s surface.
Is the height outside or inside?
In the formula, height is the perpendicular from the apex down to the base plane.