🔺 圆锥计算器（体积、侧面积、表面积、母线、由体积反求高）Cone Calculator (Volume, Lateral and Total Surface Area, Slant Height, Height from Volume)

使用说明与常见问题How-to & FAQ

「圆锥计算器（体积、侧面积、表面积、母线、由体积反求高）」是什么？What is the Cone Calculator (Volume, Lateral and Total Surface Area, Slant Height, Height from Volume) tool?

圆锥的体积 V = πr²h/3、母线 l = √(r² + h²)、侧面积 πrl、表面积 πr(r + l) 和顶角。已知量可以是半径和高、半径和母线，或半径和体积（反求高）。本地处理。Cone volume V = πr²h/3, slant height l = √(r² + h²), lateral area πrl, total surface area πr(r + l) and apex angle. Start from radius and height, radius and slant height, or radius and volume (solves for the height). Processed locally.

如何使用「圆锥计算器（体积、侧面积、表面积、母线、由体积反求高）」？How do I use the Cone Calculator (Volume, Lateral and Total Surface Area, Slant Height, Height from Volume) tool?

在「圆锥计算器（体积、侧面积、表面积、母线、由体积反求高）」中，填写「已知」、「底面半径 r」、「高 h」、「母线 l」、「体积 V」等参数，结果会随输入实时计算并显示在下方。In the Cone Calculator (Volume, Lateral and Total Surface Area, Slant Height, Height from Volume): Fill in "Known", "Base radius r", "Height h", "Slant height l", "Volume V"; results are recalculated instantly as you type.

圆锥体积公式是什么？What is the cone volume formula?

V = πr²h ÷ 3，即同底同高圆柱体积的三分之一。r = 3、h = 4 时 V = π × 9 × 4 ÷ 3 = 12π ≈ 37.70。V = πr²h ÷ 3, one third of the cylinder with the same base and height. For r = 3 and h = 4, V = π × 9 × 4 ÷ 3 = 12π ≈ 37.70.

能举个计算实例吗？Can you show a worked example?

例如在「圆锥计算器（体积、侧面积、表面积、母线、由体积反求高）」中填 已知 = 半径和高，底面半径 r = 3，高 h = 4，结果区显示：体积：37.699112；高：4；母线：5；侧面积：47.12389；底面积：28.274334；表面积：75.398224；顶角：73.7398°For example, entering Known = Radius and height, Base radius r = 3, Height h = 4 in the Cone Calculator (Volume, Lateral and Total Surface Area, Slant Height, Height from Volume) gives: Volume: 37.699112; Height: 4; Slant height: 5; Lateral area: 47.12389; Base area: 28.274334; Total surface area: 75.398224; Apex angle: 73.7398°

哪些输入会被检查？Which inputs are validated?

「圆锥计算器（体积、侧面积、表面积、母线、由体积反求高）」会检查这些输入——「底面半径 r」：必须填写，须大于 0且不大于 1,000,000,000；「高 h」：须大于 0且不大于 1,000,000,000；「母线 l」：须大于 0且不大于 1,000,000,000；「体积 V」：须大于 0且不大于 1,000,000,000,000,000,013,287,555,072；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 Cone Calculator (Volume, Lateral and Total Surface Area, Slant Height, Height from Volume) checks its inputs — "Base radius r": required, must be more than 0 and at most 1,000,000,000; "Height h": must be more than 0 and at most 1,000,000,000; "Slant height l": must be more than 0 and at most 1,000,000,000; "Volume V": must be more than 0 and at most 1,000,000,000,000,000,013,287,555,072; 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?

「圆锥计算器（体积、侧面积、表面积、母线、由体积反求高）」的设置：「已知」可选 半径和高、半径和母线、半径和体积（默认 半径和高）；「底面半径 r」默认 3；「高 h」默认 4；「母线 l」默认 5；「体积 V」默认 37.7。每次生成结果都按当前设置处理。Settings in the Cone Calculator (Volume, Lateral and Total Surface Area, Slant Height, Height from Volume) — "Known": Radius and height, Radius and slant height, Radius and volume (default Radius and height); "Base radius r" default 3; "Height h" default 4; "Slant height l" default 5; "Volume V" default 37.7. The result always uses the current settings.

计算精度如何？How precise are the results?

「圆锥计算器（体积、侧面积、表面积、母线、由体积反求高）」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 Cone Calculator (Volume, Lateral and Total Surface Area, Slant Height, Height from Volume) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「圆锥计算器（体积、侧面积、表面积、母线、由体积反求高）」免费吗？需要注册吗？Is the Cone Calculator (Volume, Lateral and Total Surface Area, Slant Height, Height from Volume) free? Do I need an account?

「圆锥计算器（体积、侧面积、表面积、母线、由体积反求高）」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 Cone Calculator (Volume, Lateral and Total Surface Area, Slant Height, Height from Volume) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.