THE NUMBERS, EXPLAINED
How to use this calculator.
A right circular cone. Slant height is not the perpendicular height.
Start with your inputs
Enter radius, perpendicular height. Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Radius | 3 |
| Perpendicular height | 4 |
A worked example
With the example inputs above, volume is 37.699112. Change the inputs to explore your own scenario.
Putting the example numbers into the formula
Volume
π × (3) × (3) × (4) ÷ 3 = 37.699112
Slant height
hypot((3),(4)) = 5
Surface area
π × (3) × ((3)+hypot((3),(4))) = 75.398224
| Result | Example answer |
|---|---|
| Volume | 37.699112 |
| Slant height | 5 |
| Surface area | 75.398224 |
How this is calculated
Volume
π × a × a × b ÷ 3
Slant height
hypot(a,b)
Surface area
π × a × (a+hypot(a,b))
Symbols and units
- a
- Radius
- b
- Perpendicular height
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Calculation steps and notation
π is the circle constant, approximately 3.141592653589793.
hypot(x, y, …) is sqrt(x²+y²+…), the Euclidean length.
Assumptions and limits
A right circular cone. Slant height is not the perpendicular height.
Calculations use the values you enter. Blank or invalid inputs show an error instead of silently substituting zero. Results are displayed to useful precision; calculations retain the underlying numeric precision.
Questions about this tool
What does the result tell me?
Volume; Slant height; Surface area. The result applies to the method and inputs described above. Check the units and assumptions before using it in a decision.
Why might another calculator differ?
Differences in units, rounding, timing or model definitions can produce different answers. Compare the input definitions and the method, rather than only the final number. For this tool: A right circular cone. Slant height is not the perpendicular height.
Are my inputs stored or sent to AI?
Calculations on this page happen in your browser. The separate AI question finder sends its submitted conversation to OpenAI; these calculator fields are not sent. Favourites and recent tool names are stored locally. A shared link contains the inputs you choose to include.
Further reading
Background reading; this does not imply endorsement or independent review of SumFizz.
Review status
Software example and browser checks are recorded in our quality report. No external expert review is claimed. Created with coding assistance; calculations run as ordinary browser code.
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