全部书籍

1 Primary & Middle School Mathematics1–9 年级在线 2 High School Mathematics10–12 年级在线 3 University Mathematics — Year 1本科一年级在线 4 University Mathematics — Year 2本科二年级在线 5 University Mathematics — Year 3本科三年级在线

1 Primary & Middle School Physics1–9 年级在线 2 High School Physics10–12 年级在线 3 University Physics — Year 1本科一年级在线 4 University Physics — Year 2本科二年级在线 5 University Physics — Year 3本科三年级在线

1 School Chemistry — Grades 1 to 121–12 年级在线 2 University Chemistry — Year 1本科一年级在线 3 University Chemistry — Year 2本科二年级在线 4 University Chemistry — Year 3本科三年级在线

1 Primary & Middle School Biology1–9 年级在线 2 High School Biology10–12 年级在线 3 University Biology — Year 1本科一年级在线 4 University Biology — Year 2本科二年级在线 5 University Biology — Year 3本科三年级在线

1 Primary & Middle School Earth and Space Sciences1–9 年级在线 2 High School Earth and Space Sciences10–12 年级在线 3 University Earth and Space Sciences — Year 1本科一年级在线 4 University Earth and Space Sciences — Year 2本科二年级在线 5 University Earth and Space Sciences — Year 3本科三年级在线

1 Markets I: The Ecosystem and Exchange-Traded Markets市场在线 2 Markets II: Rates, FX and Credit市场在线 3 Markets III: Commodities, Energy and Crypto市场在线 4 Quantitative Methods方法在线 5 Derivatives and Volatility衍生品在线 6 Rates, Credit, XVA and Risk利率、信用与风险在线 7 Research Craft: Predictors, Backtests, Measurement, Portfolios研究在线 8 Strategies I: Equities and Futures策略在线 9 Strategies II: Volatility, Relative Value, Macro and the Bank Desks策略在线 10 Microstructure and Execution交易执行在线 11 Market Making and High-Frequency Trading做市在线 12 Machine Learning for Markets机器学习在线 13 Low-Latency Software技术在线 14 Networks, Hardware and Trading Infrastructure技术在线 15 Research, Data and Risk Platforms技术在线 16 The Desk and the Firm公司运营在线 17 The Industry: Firms, Roles and Careers职业发展在线 18 Interviews I: Maths, Probability and Speed职业发展在线 19 Interviews II: Markets, Trading Games and the Final Round职业发展在线 20 Interviews III: Code职业发展在线

全部游戏 Math Fuse Word Reactor Atlas Dash

应用关于

Coach

English Français Español Nederlands Português हिन्दी العربية Bahasa Indonesia 简体中文 বাংলা

登录开始阅读

书籍暂未推出简体中文版——当前显示英文版。

Mathematics · 术语表

什么是 Pyramid, cone？

又称： pyramid · cone

Definition 62.1 Primary & Middle School Mathematics · 第 62 章 — Pyramids and Cones

A pyramid has a polygon as its base and a point, the apex, joined to every vertex of the base by triangular faces. Its height is the distance from the apex to the plane of the base.
A cone is the same construction over a disk: a base disk, an apex, and a curved lateral surface.

A pyramid is regular when its base is a regular polygon (square, equilateral triangle, …) and its apex sits vertically above the center of the base.

A square-based pyramid and a cone: one polygonal or circular base, one apex, and the height measured perpendicular to the base.

示例

Example 62.2 (Counting faces, edges, vertices)

A pyramid with a square base has $5$ faces ( $1$ square $+ 4$ triangles), $8$ edges and $5$ vertices. With an $n$ -sided base: $n + 1$ faces, $2n$ edges, $n + 1$ vertices. Check Euler’s little pattern: faces $+$ vertices $=$ edges $+ 2$ .

Example 62.5

A pyramid has a square base of side $5$ cm and height $9$ cm:

base area: $B = 5^2 = 25$ cm $^2$ ;
volume: $V = \frac13 \times 25 \times 9 = 25 \times 3 = 75$ cm $^3$ .

An ice-cream cone of radius $3$ cm and height $10$ cm:

V = \frac13 \times \pi \times 3^2 \times 10 = 30\pi \approx 94 \text{ cm}^3 .

Example 62.6 (Careful with the height)

For a cone, do not confuse the height $h$ (apex to center of the base, perpendicular) with the slant height $s$ (apex to the rim). They are related by Pythagoras (Theorem 58.1) in the right triangle apex–center–rim:

s^2 = h^2 + r^2 .

A cone with $r = 3$ and $s = 5$ therefore has height $h = \sqrt{25 - 9} = 4$ , and volume $\frac13 \pi \times 9 \times 4 = 12\pi$ .

在原文中阅读 →