Cone Volume Calculator
The volume of a cone from its base radius and height.
Result
Volume
261.80
How it works
A cone's volume is one third of the cylinder that would enclose it: V = (1/3)·π·r²·h. With a radius of 5 and a height of 12, the volume is about 314. The one third is not arbitrary. Fill a cone with water and pour it into a cylinder of the same base and height, and you will need exactly three cones to fill it — a result the Greeks proved geometrically and calculus later confirmed. The same factor of a third appears for a pyramid inside its prism. Use consistent units and the answer follows: centimetres in, cubic centimetres out, and 1,000 cm³ to the litre. Everyday cones are everywhere once you look — ice-cream cones, funnels, traffic cones, grain piles, and the conical roofs whose material you might need to estimate.
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Frequently asked questions
Why one third?
A cone is one third of a cylinder of equal base and height — that is the (1/3) factor.
What units does it use?
Whatever you enter: if radius and height are in cm, the volume is in cm³.
How do I find the surface area of a cone?
Total area = πr² + πrl, where l is the slant height √(r² + h²). The first term is the circular base, the second the curved side unrolled into a sector.
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