Cone Volume
Calculate the volume of a right circular cone using radius and height with the formula V = (1/3)pir^2h. Free online 3D geometry calculator with visual breakdown chart for students and professionals.
About This Calculator
This Cone Volume Calculator computes the volume of a right circular cone using its radius and height. The formula V = (1/3)pir^2h shows that a cone holds exactly one-third of the volume of a cylinder with the same base and height.
The breakdown chart visualizes how the base area (pir^2) and height combine with the one-third factor to produce the final volume. This calculator is ideal for geometry students, architects, and anyone working with conical shapes.
Real-world applications:
- Construction -- calculating concrete volume for cone-shaped foundations
- Cooking -- measuring volume of conical containers and funnels
- Industry -- calculating hopper and silo volumes
- Education -- teaching 3D geometry and the relationship between cones and cylinders
Frequently Asked Questions
What is the formula for cone volume?
The formula for the volume of a right circular cone is V = (1/3)pir^2h, where r is the radius of the circular base and h is the vertical height from the center of the base to the apex. A cone holds exactly one-third the volume of a cylinder with the same base and height.
How is cone volume different from cylinder volume?
A cone has exactly one-third the volume of a cylinder with the same base radius and height. This is because the cone's cross-sectional area decreases linearly from base to apex, while a cylinder's cross-sectional area remains constant. So V_cone = (1/3) x V_cylinder.
What units should I use for cone volume?
You can use any consistent unit for radius and height (inches, feet, cm, meters, etc.). The volume will be in cubic units of whatever unit you choose. For example, cm and cm give cm^3, feet and feet give ft^3. This calculator accepts any numeric input for both fields.
How do I find the radius of a cone?
If you know the diameter of the cone's base, divide by 2 to get the radius. If you know the circumference, divide by 2pi. If you know the slant height (l) and the vertical height (h), use the Pythagorean theorem: r = sqrt(l^2 - h^2).
What is the volume of a cone with radius 5 and height 10?
Using V = (1/3)pir^2h: V = (1/3) x pi x 5^2 x 10 = (1/3) x pi x 25 x 10 = (1/3) x 785.4 = 261.8 cubic units. So a cone with radius 5 and height 10 has a volume of approximately 261.8 cubic units.
Is this tool free to use?
Yes, all calculators on Calculy are completely free to use with no registration required. You can also share your calculation results via URL.