Cone Calculator
Cone Volume and Surface Area Calculator
Calculate the volume and surface area of a cone with our easy-to-use calculator. Learn about cone formulas, real-world applications, and explore interactive examples.
A cone is a three-dimensional geometric shape that tapers smoothly from a flat circular base to a point called the apex or vertex. Our cone calculator helps you determine both the volume and surface area of a cone using its radius and height. Perfect for engineering, architecture, and educational purposes.
Formula
Volume = (1/3)πr²h
Surface Area = πr² + πr√(r² + h²)
Where:
- r:radius of the circular base (in your chosen unit of length)
- h:height of the cone (in your chosen unit of length)
- π:pi, approximately equal to 3.14159
How to Calculate Cone Volume
To calculate the volume of a cone, use one-third of the product of the base area (πr²) and height...
Real-World Applications
Cones appear in various applications from ice cream cones to traffic cones...
Frequently Asked Questions
Why is the volume one-third of a cylinder?
A cone has one-third the volume of a cylinder with the same base and height due to the way it tapers to a point, as proven by Cavalieri's principle.
What is slant height?
Slant height (s) is the distance from any point on the edge of the base to the apex. It can be calculated using the Pythagorean theorem: s = √(r² + h²).