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Cone Curved Surface Area and Closed Total

Cone Curved Surface Area and Closed Total. Convert compatible units, recover unknown dimensions and distinguish curved surfaces, bases and total measures.

  • Formula & worked example
  • Private in your browser
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Example in initial displayed units: Radius (r) 3, Height (h) 4 gives Slant height (l) 5, Base area (A_B) 28.274334, Lateral surface area (A_L) 47.12389, Surface area (A) 75.398224, Volume (V) 37.699112.

Alateral = πrs; Abase = πr²; Atotal = Alateral+Abase

Worked example

Enter these known values and leave the other values blank.

Radius (r)
3 cm
Height (h)
4 cm
Slant height (l)
5 cm
Lateral surface area (A_L)
47.12 cm²
Surface area (A)
75.4 cm²
Base area (A_B)
28.274 cm²
Volume (V)
37.7 cm³

Assumptions and limitations

  • A right circular cone has perpendicular height h and slant length s. Total area includes one flat circular base; lateral area includes only the curved surface. Radius and height must be positive.
  • Select units before entering dimensions. Clear an unknown result before solving backward, and supply enough independent measurements. Display rounding does not represent measurement uncertainty.
  • Calculations use 64 significant digits and full-precision π. Original reference drawings explain dimensions and are not drawn to the entered scale.

Common questions

Which cone area excludes the base?

Lateral area πrs covers the curved surface only. Add πr² for the closed cone total.

References

Require positive physical dimensions and real nondegenerate inverse roots while preserving documented limiting shapes. The US fluid ounce uses one 128th of the exact US liquid gallon, replacing the rounded captured reciprocal factor. Bookify replaces the captured rounded US gallon with the exact 3.785411784-liter definition.

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