Description
Return hypot(height, firstRadius-secondRadius) for slantHeight.
Solid-geometry formulas assume particular shapes and measurement directions. Axial height, slant length, filled-volume centroid, and surface centroid are different quantities even when they describe the same object.
Return hypot(height, firstRadius-secondRadius) for slantHeight.
When to use this tool
Use Frustum Slant Height From Generators when you need a local dimension, area, or centroid term for the stated ideal solid.
How to use the tool and how it works
- Enter height, firstRadius, secondRadius. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read slantHeight. Use the output convention below.
Require nonnegative height and two radii. Return hypot(height, firstRadius-secondRadius) for slantHeight.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| height | Height in the common length unit and direction stated above. | Required. Finite number; minimum 0. |
| firstRadius | First Radius | Required. Finite number; minimum 0. |
| secondRadius | Second Radius | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| slantHeight | Slant Height | Required. Finite number. |
{
"input": {
"height": 4,
"firstRadius": 5,
"secondRadius": 2
},
"output": {
"slantHeight": 5
}
}Limitations and assumptions
- The formula assumes a coaxial right circular frustum with axial perpendicular height; all lengths share units and no oblique generator, actual solid, or structural suitability is verified.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use a complete solid model for clipping, oblique shapes, or nonuniform material. Confirm radius, height, and centroid conventions before applying an ideal-shape identity.
References
Similar or alternative tools
- Cone Apex Angle Radius Height
Return atan2(radius,height) as halfAngle and twice it as apexAngle.
- Geometry: Cone Generatrix Angle From Radii
Return atan2(absolute radius difference,height) in degrees and the corresponding hypotenuse as slantLength inside result.