Cone Formula & The 1/3 Rule
A cone has exactly one-third the volume of a cylinder with the same base radius and height. This is a fundamental constant in geometry.
Visualizing the Formula
Imagine a cylinder and a cone with the same dimensions. If you filled the cone with water and poured it into the cylinder, it would take exactly three full cones to fill the cylinder.
Cone Volume Guide Guide
How to Use
- 1Enter the **Radius (r)** of the circular base.
- 2Enter the **Height (h)** of the cone.
- 3Click calculate to find the **Volume (V)**.
Formula & Logic
The volume of a cone is exactly one-third the volume of a cylinder with the same base radius and height. This geometric relationship holds true for all right circular cones.
Practical Applications
Construction
Calculate the volume of sand or gravel piles, which naturally form a conical shape.
Food Industry
Estimate the filling capacity of waffle cones or funnel-shaped containers.
Manufacturing
Determine the material needed to cast conical parts or components.
Frequently Asked Questions
Q.What is a right circular cone?
A right circular cone is a cone where the axis (height) is perpendicular to the base, meaning the tip is directly above the center of the circle.
Q.How do I find the radius if I only have the diameter?
Simply divide the diameter by 2. Radius = Diameter / 2.
Q.Does the slant height matter for volume?
No, the volume formula depends only on the vertical height and the radius. Slant height is used for surface area calculations.