🌗 半球体积计算器（含表面积）Volume of a Hemisphere Calculator (with Surface Area)
实心半球体积 V = (2/3) π r³，含底表面积 3 π r²（曲面 2 π r² + 底面 π r²）。半径须大于 0。本地处理。Solid hemisphere volume V = (2/3) π r³, and surface area including the base 3 π r² (curved 2 π r² + base π r²). Radius must be greater than 0. Processed locally.
使用说明与常见问题How-to & FAQ
「半球体积计算器（含表面积）」是什么？What is the Volume of a Hemisphere Calculator (with Surface Area) tool?
实心半球体积 V = (2/3) π r³，含底表面积 3 π r²（曲面 2 π r² + 底面 π r²）。半径须大于 0。本地处理。Solid hemisphere volume V = (2/3) π r³, and surface area including the base 3 π r² (curved 2 π r² + base π r²). Radius must be greater than 0. Processed locally.
如何使用「半球体积计算器（含表面积）」？How do I use the Volume of a Hemisphere Calculator (with Surface Area) tool?
在「半球体积计算器（含表面积）」中，填写「半径」等参数，结果会随输入实时计算并显示在下方。In the Volume of a Hemisphere Calculator (with Surface Area): Fill in "Radius"; results are recalculated instantly as you type.
空心半球呢？What about a hollow hemisphere?
本页按实心半球。薄壳可用外半径体积减内半径体积近似。This page is a solid hemisphere. For a thin shell, subtract the inner-radius volume from the outer-radius volume.
和整球的关系？How does it relate to a full sphere?
整球体积 (4/3)πr³ 的一半是 (2/3)πr³，正是半球体积。Half of a full sphere (4/3)πr³ is (2/3)πr³ - the hemisphere volume.
能举个计算实例吗？Can you show a worked example?
例如在「半球体积计算器（含表面积）」中填 半径 = 6，结果区显示：体积：452.389342；表面积（含底）：339.292007For example, entering Radius = 6 in the Volume of a Hemisphere Calculator (with Surface Area) gives: Volume: 452.389342; Surface (with base): 339.292007
哪些输入会被检查？Which inputs are validated?
「半球体积计算器（含表面积）」会检查这些输入——「半径」：必须填写，须大于 0且不大于 1,000,000,000,000,000；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Volume of a Hemisphere Calculator (with Surface Area) checks its inputs — "Radius": required, must be more than 0 and at most 1,000,000,000,000,000; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.
有哪些选项可以调整？What options can I adjust?
「半球体积计算器（含表面积）」的设置：「半径」默认 6。每次生成结果都按当前设置处理。Settings in the Volume of a Hemisphere Calculator (with Surface Area) — "Radius" default 6. The result always uses the current settings.
计算精度如何？How precise are the results?
「半球体积计算器（含表面积）」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Volume of a Hemisphere Calculator (with Surface Area) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「半球体积计算器（含表面积）」免费吗？需要注册吗？Is the Volume of a Hemisphere Calculator (with Surface Area) free? Do I need an account?
「半球体积计算器（含表面积）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Volume of a Hemisphere Calculator (with Surface Area) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.