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Hemisphere Curved Area, Flat Base and Total Surface

Hemisphere Curved Area, Flat Base and Total Surface. 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 3 gives Diameter 6, Volume 56.548668, Flat circular base area 28.274334, Curved hemisphere area 56.548668, Total area including base 84.823002, Surface to volume ratio "1.5".

Acurved = 2πr²; Atotal = 3πr²; V = 2πr³/3; Atotal/V = 9/(2r)

Worked example

Enter these known values and leave the other values blank.

Radius
3 cm
Diameter
6 cm
Volume
56.5 cm³
Surface to volume ratio
1.5 1/ cm
Flat circular base area
28.3 cm²
Curved hemisphere area
56.55 cm²
Total area including base
84.82 cm²

Assumptions and limitations

  • A hemisphere is half a sphere cut through its center. Curved area excludes the flat disk; total area includes it. The surface-to-volume ratio uses total area and has inverse-length units.
  • 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

Does hemisphere total area include the flat base?

Yes. Total area is 3πr², comprising the curved half-sphere area 2πr² plus the circular base πr².

References

The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor. The cubic international mile uses the cube of the exact 1609.344-meter mile, replacing a rounded reciprocal factor.

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