📚 Surface Area and Volume of Cuboids and Prisms | 长方体与棱柱的表面积和体积
In KS3 Cambridge Mathematics, surface area and volume of cuboids and prisms are core practical skills. They connect arithmetic, algebra and geometry to real-world tasks such as packaging, construction and design. This revision article explains the essential formulas, units, worked examples and exam techniques you need.
在 KS3 剑桥数学中，长方体与棱柱的表面积和体积是核心的实用技能。它们将算术、代数和几何与包装、建筑和设计等现实任务联系起来。本复习文章讲解你需要掌握的基本公式、单位、例题和考试技巧。
1. Understanding Cuboids and Prisms | 认识长方体与棱柱
A cuboid is a 3D shape made of six rectangular faces. All angles in a cuboid are right angles. Opposite faces are congruent, meaning they have the same shape and size. A prism is any 3D shape with a constant cross-section that runs along its entire length. A cuboid is a special type of prism with a rectangular cross-section.
长方体是由六个矩形面组成的三维图形。长方体的所有角都是直角。相对的面全等，即形状和大小完全一致。棱柱是任何横截面沿全长保持不变的三维图形。长方体是一种具有矩形横截面的特殊棱柱。
- Cuboid dimensions: length l, width w, height h - 长方体尺寸：长 l、宽 w、高 h
- Prism: a uniform cross-section and a length - 棱柱：均匀的横截面和一条长度
- Examples of prisms: triangular prism, cube, hexagonal prism - 棱柱举例：三棱柱、正方体、六棱柱
2. Surface Area of a Cuboid | 长方体的表面积
The surface area of a cuboid is the total area of all six faces. Because opposite faces are identical, you only need to consider three distinct rectangles and then multiply by 2. If the length is l, width is w and height is h, the areas are lw, lh and wh for the three different pairs.
长方体的表面积是所有六个面的面积之和。由于相对的面完全相同，你只需考虑三个不同的矩形，然后乘以 2。如果长为 l、宽为 w、高为 h，那么三种不同面的面积分别是 lw、lh 和 wh。
