Overview
A cone has a circular base and a single apex, formed by rotating a right triangle around one leg. Its volume is one third of a cylinder with the same base and height, and its lateral area depends on the slant height.
Formula
Volume = (1/3)πr²h, slant height l = √(r² + h²), total area = πr² + πrl.
How it works
Enter radius and height
The height is perpendicular to the base.
Compute the slant height
l = √(r² + h²).
Compute the volume
One third of the base area times the height.
Compute the area
Add the base area to the lateral area.
Worked examples
Example 1: radius 3 and height 4
Slant height 5, volume ≈ 37.6991, total area ≈ 75.3982.
Example 2: radius 6 and height 8
Slant height 10, volume ≈ 301.5929, total area ≈ 414.6902.
Frequently asked questions
What is the difference between height and slant height?
Height is perpendicular to the base, while slant height runs from the apex to the base circumference.
Why is the volume one third of the cylinder?
Because three cone volumes fill a cylinder with the same base and height.
Does total surface area include the base?
Yes. Total area = base area + lateral area.
This calculator is for educational and informational purposes only and is not a substitute for professional advice.