Cone Volume Calculator
Calculate the volume of a right circular cone given its radius and height. Perfect for 3D geometry calculations.
Calculate Cone Volume
Enter the radius and height of the cone:
Cone Volume Formula
The volume of a cone is calculated using the formula:
Understanding Cone Volume
A cone's volume is exactly one-third the volume of a cylinder with the same base radius and height. This makes sense because you can fit exactly three cones inside a cylinder of the same dimensions.
Example Calculation
For a cone with radius 3 cm and height 7 cm:
Volume = ⅓ × 3.14159 × 9 × 7
Volume = ⅓ × 197.92083
Volume = 65.97361 cm³
Comparison with Cylinder
A cylinder with the same radius and height would have:
Cylinder Volume = π × 3² × 7 = 197.92083 cm³
The cone volume (65.97361 cm³) is exactly ⅓ of the cylinder volume (197.92083 cm³).
Common Cone Volumes
| Radius | Height | Volume |
|---|---|---|
| 2 units | 5 units | 20.94 units³ |
| 3 units | 7 units | 65.97 units³ |
| 5 units | 10 units | 261.80 units³ |
| 8 units | 12 units | 804.25 units³ |
Applications
Cone volume calculations are used in:
- 🏭 Manufacturing: Calculating material volumes for conical containers
- 🍦 Food Industry: Ice cream cone volume calculations
- 🏗️ Construction: Concrete volume for conical foundations
- 🔬 Science: Volume calculations for laboratory equipment
💡 Tip: Remember that this formula is for right circular cones. For oblique cones (where the axis is not perpendicular to the base), the formula is more complex and requires additional measurements.