Hemisphere curved area
Hemisphere curved surface S = 2πr²: enter the radius to get the curved area plus base area, total surface and volume; values are rounded to 6 decimals and a non-positive radius is rejected.
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Result
One quantity per line, ready to copy.
Enter a radius to calculate
What this tool does
- Check the curved area of a hemispherical container and get the curved and total surface for coating or cutting.
- Compare a hemisphere with a full sphere of the same radius: half the volume, and 3πr² of total surface (three quarters of the sphere).
- Verify the formulas: curved 2πr², base πr², total 3πr², volume 2πr³/3.
Example
Input
2
Output
半径 2 的半球曲面面积：25.132741 底面圆面积 πr²：12.566371 总表面积 3πr²：37.699112 半球体积 2πr³/3：16.755161 长度单位 u，面积 u²，体积 u³
At radius 1 the hemisphere volume is 2π/3 ≈ 2.094395, the curved surface 2π ≈ 6.283185, the base π ≈ 3.141593 and the total surface 3π ≈ 9.424778 — all canonical.
Frequently asked questions
Why is the total surface 3πr²?
The curved part is 2πr² (half the sphere) and the flat base adds πr², giving 3πr². A dome without a base uses only 2πr².
Is the volume exactly half?
Yes. The flat face cuts the sphere in half, so the volume is half of 4πr³/3, namely 2πr³/3.
What if the radius is 0?
It reports an error. A zero radius collapses the hemisphere into a point — the formula still evaluates but the answer is meaningless, so non-positive input is rejected.
Keywords：半球曲面面积Hemisphere curved area半球hemisphere几何计算geometry曲面面积