Cone Calculator
Find a cone's volume, slant height and surface area.
Cone measurements from base radius and height.
How the Math Works
The Cone Calculator uses two fundamental formulas to analyze cones. The volume formula V = 1/3 π r² h calculates the space inside a cone by multiplying one-third of π with the base radius squared and the height. The slant height formula slant = √(r² + h²) applies the Pythagorean theorem to find the distance from the apex to the base edge. These formulas work together to provide complete geometric analysis, with surface area derived by combining the base area (πr²) and lateral surface area (πr√(r² + h²)).
Practical Applications
This calculator is essential for engineers designing conical structures like silos, funnels, or architectural features. Manufacturers use it to determine material requirements for conical containers, while construction professionals calculate concrete volumes for pyramid-shaped foundations. Students and teachers rely on it for geometry homework involving real-world cone problems, ensuring accurate solutions without manual computation errors.
Day-to-Day Use
In daily life, this tool helps estimate capacities of household items like sugar cones, bird feeders, or planters. It's useful for DIY projects involving conical decorations, party supplies, or crafts, where calculating paint coverage or material needs saves time and money. Even when shopping, understanding cone volumes helps compare container sizes for food storage or gardening supplies.
Worked example
r 3, h 9 → volume 84.8, slant 9.49.
FAQ
Why 1/3?
A cone holds exactly one-third of the cylinder with the same base and height.