Geometry
Cone Volume Calculator
Volume, slant height, and surface area of cones. Calculate the volume, lateral surface area, and slant height of any right circular cone from radius and height.
Live Vector System
Core Dimensions
Analytic Metrics
Surface Area
78.54
Perimeter
31.416
Mathematical Verification
Our engine utilizes double-precision floating-point arithmetic for geometric derivations. For triangles, we implement Heron's Theorem with strict validation to ensure the triangle inequality principle is maintained.
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Solution Methodology
01
Enter Radius & Height
Provide the base radius r and vertical height h.
02
Compute Slant Height
Calculate l = √(r² + h²) as the lateral edge length.
03
Apply Volume & Area Formulas
Evaluate V = (1/3)πr²h, L = πrl, and SA = πr(r + l).
Common Questions
How do you calculate the volume of a cone?
Volume = (1/3)πr²h. A cone holds exactly one-third the volume of a cylinder with the same base radius and height, which is why the 1/3 factor appears in the formula.
What is slant height and how is it found?
Slant height l is the distance from the apex to any point on the base circumference, measured along the lateral surface. It is found using the Pythagorean theorem: l = √(r² + h²).