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Truncated Cone Volume Calculator — result sheet
Calculate the volume, slant height, lateral area, and total surface area of a right circular truncated cone.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: V = πh(R²+Rr+r²)/3; l = √(h²+(R-r)²); lateral = π(R+r)l; total = lateral + πR² + πr².
A truncated cone, or frustum, is the portion left after cutting a cone parallel to its base. The calculator reports capacity and both curved and complete surface areas.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Larger radius R — units; minimum 1.0E-6; maximum 1000000000
- Smaller radius r — units; minimum 1.0E-6; maximum 1000000000
- Vertical height — units; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Larger radius R | 5 |
| Smaller radius r | 3 |
| Vertical height | 4 |
Volume: about 201.06 cubic units; slant height: about 4.47 units.
Assumptions and limits
- R is at least r and the shape is a right circular frustum with parallel circular ends.
- The height is measured along the central axis and all dimensions use one unit.
- Total surface includes both circular ends; wall thickness, rims, and usable fill limits are excluded.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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