How this calculation works
Use the perpendicular height, not the slant height. A cone has one third of the volume of a cylinder with the same base and height.
Volume = πr²h/3A worked example
A radius of 3 and height of 10 gives approximately 94.247780 cubic units.
Good to know
Uses the stated formula and assumptions. Displayed decimal values are rounded; use consistent units for all inputs.
A cone holds one third of a matching cylinder
A cone and cylinder sharing the same circular base and perpendicular height have volumes in a 1:3 ratio. That is why the cylinder volume πr²h becomes πr²h/3 for the cone.
Doubling both radius and height multiplies the cone’s volume by eight. The scaling follows three length dimensions, not the apparent size of a two-dimensional drawing.
Slant height answers a different question
The distance along the side from rim to tip is a slant height. The formula here needs the perpendicular base-to-tip height. For a right cone, radius, perpendicular height and slant height form a right triangle.
A cone with its top cut off is a frustum and needs a different formula involving both radii. Do not use the full-cone volume unless the missing portion is separately accounted for.
A few questions, answered
Does this return surface area?
No. It returns full cone volume only.
Does radius mean the width of the base?
No. Radius is half the circular base’s diameter.