🪣 圆台计算器（体积、母线、侧面积、表面积、容积升数）Conical Frustum Calculator (Volume, Slant Height, Lateral and Surface Area, Capacity in Litres)
圆台（截头圆锥）体积 V = πh(R² + Rr + r²)/3，母线 s = √((R − r)² + h²)，侧面积 π(R + r)s，表面积再加两个底面；以厘米为单位时还给出容积（升），适合水桶、花盆等。本地处理。Conical frustum (truncated cone) volume V = πh(R² + Rr + r²)/3, slant height s = √((R − r)² + h²), lateral area π(R + r)s and total surface area including both bases; in centimetres it also gives the capacity in litres, handy for buckets and planters. Processed locally.
使用说明与常见问题How-to & FAQ
「圆台计算器（体积、母线、侧面积、表面积、容积升数）」是什么？What is the Conical Frustum Calculator (Volume, Slant Height, Lateral and Surface Area, Capacity in Litres) tool?
圆台（截头圆锥）体积 V = πh(R² + Rr + r²)/3，母线 s = √((R − r)² + h²)，侧面积 π(R + r)s，表面积再加两个底面；以厘米为单位时还给出容积（升），适合水桶、花盆等。本地处理。Conical frustum (truncated cone) volume V = πh(R² + Rr + r²)/3, slant height s = √((R − r)² + h²), lateral area π(R + r)s and total surface area including both bases; in centimetres it also gives the capacity in litres, handy for buckets and planters. Processed locally.
如何使用「圆台计算器（体积、母线、侧面积、表面积、容积升数）」？How do I use the Conical Frustum Calculator (Volume, Slant Height, Lateral and Surface Area, Capacity in Litres) tool?
在「圆台计算器（体积、母线、侧面积、表面积、容积升数）」中，填写「下底半径 R」、「上底半径 r」、「高 h」、「单位」等参数，结果会随输入实时计算并显示在下方。In the Conical Frustum Calculator (Volume, Slant Height, Lateral and Surface Area, Capacity in Litres): Fill in "Bottom radius R", "Top radius r", "Height h", "Units"; results are recalculated instantly as you type.
圆台体积怎么算？How is the frustum volume calculated?
V = πh(R² + Rr + r²) ÷ 3。R = 15 cm、r = 10 cm、h = 30 cm 的桶：π × 30 × (225 + 150 + 100) ÷ 3 ≈ 14,923 cm³ ≈ 14.9 升。V = πh(R² + Rr + r²) ÷ 3. A bucket with R = 15 cm, r = 10 cm and h = 30 cm holds π × 30 × (225 + 150 + 100) ÷ 3 ≈ 14,923 cm³ ≈ 14.9 L.
能举个计算实例吗？Can you show a worked example?
例如在「圆台计算器（体积、母线、侧面积、表面积、容积升数）」中填 下底半径 R = 15，上底半径 r = 10，高 h = 30，单位 = 厘米，结果区显示：体积：14,922.565105 cm³；母线：30.413813 cm；侧面积：2,388.69526 cm²；表面积（含两底）：3,409.712872 cm²；容积：14.9226 升For example, entering Bottom radius R = 15, Top radius r = 10, Height h = 30, Units = cm in the Conical Frustum Calculator (Volume, Slant Height, Lateral and Surface Area, Capacity in Litres) gives: Volume: 14,922.565105 cm³; Slant height: 30.413813 cm; Lateral area: 2,388.69526 cm²; Total surface area (both bases): 3,409.712872 cm²; Capacity: 14.9226 L
哪些输入会被检查？Which inputs are validated?
「圆台计算器（体积、母线、侧面积、表面积、容积升数）」会检查这些输入——「下底半径 R」：必须填写，须不小于 0且不大于 1,000,000,000；「上底半径 r」：必须填写，须不小于 0且不大于 1,000,000,000；「高 h」：必须填写，须大于 0且不大于 1,000,000,000；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 Conical Frustum Calculator (Volume, Slant Height, Lateral and Surface Area, Capacity in Litres) checks its inputs — "Bottom radius R": required, must be at least 0 and at most 1,000,000,000; "Top radius r": required, must be at least 0 and at most 1,000,000,000; "Height h": required, must be more than 0 and at most 1,000,000,000; 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?
「圆台计算器（体积、母线、侧面积、表面积、容积升数）」的设置：「下底半径 R」默认 15；「上底半径 r」默认 10；「高 h」默认 30；「单位」可选 厘米、米 m、英寸、无单位（默认 厘米）。每次生成结果都按当前设置处理。Settings in the Conical Frustum Calculator (Volume, Slant Height, Lateral and Surface Area, Capacity in Litres) — "Bottom radius R" default 15; "Top radius r" default 10; "Height h" default 30; "Units": 4 choices. The result always uses the current settings.
计算精度如何？How precise are the results?
「圆台计算器（体积、母线、侧面积、表面积、容积升数）」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 Conical Frustum Calculator (Volume, Slant Height, Lateral and Surface Area, Capacity in Litres) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「圆台计算器（体积、母线、侧面积、表面积、容积升数）」免费吗？需要注册吗？Is the Conical Frustum Calculator (Volume, Slant Height, Lateral and Surface Area, Capacity in Litres) free? Do I need an account?
「圆台计算器（体积、母线、侧面积、表面积、容积升数）」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 Conical Frustum Calculator (Volume, Slant Height, Lateral and Surface Area, Capacity in Litres) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.