Cone Calculator
Compute cone volume, slant height, lateral area and total surface area.
Cone Calculator
Compute cone volume, slant height, lateral area and total surface area.
How to use the Cone Calculator
- Enter the radius of the base.
- Enter the vertical height.
- Click Calculate.
Formula
Volume = 1/3 × πr²h
Slant height l = √(r² + h²)
Lateral surface = πrl
Total surface = πr(l + r)
Example
Radius 3, height 4: l = √(9+16) = 5. Volume = 1/3×π×9×4 ≈ 37.699.
Step-by-step calculation
- Slant height: √(3²+4²) = √25 = 5.
- Volume: 1/3 × π × 9 × 4 ≈ 37.699.
- Lateral: π × 3 × 5 ≈ 47.124.
- Total: π × 3 × (5+3) ≈ 75.398.
Real-world uses
- Hopper and funnel design.
- Ice cream cone volume.
- Roof and spire calculations.
Common mistakes
- Using slant height instead of vertical height in the volume formula.
- Confusing lateral and total surface area.
- Forgetting the 1/3 in the volume formula.
Frequently asked questions
What is the slant height?
The distance from the tip to the edge of the base, measured along the surface.
How is this different from a pyramid?
A cone has a circular base. A pyramid has a polygonal base. Volume is always 1/3 × base area × height.
Can I work backwards from volume?
Yes. Given volume and radius, h = 3V/(πr²).