Cuboids

A cuboid is a three-dimensional shape that has six rectangular faces. It is also known as a rectangular prism. The opposite faces of a cuboid are equal and parallel to each other. The cuboid is a special case of a rectangular prism where all edges are at right angles.

Characteristics of a Cuboid

• 6 faces: A cuboid has 6 faces, each of which is a rectangle
• 12 edges: It has 12 edges where each edge meets another edge at a corner
• 8 vertices: A cuboid has 8 vertices or corners where 3 edges meet
• Opposite faces are equal and parallel

Formulas for Cuboids

• Surface Area of a Cuboid = 2(lw + wh + lh) where l, w, and h are the length, width, and height of the cuboid respectively
• Volume of a Cuboid = l × w × h where l, w, and h are the length, width, and height of the cuboid respectively

Example Problems

1. Find the surface area and volume of a cuboid with length 5 cm, width 3 cm, and height 4 cm.

Surface Area = 2(5*3 + 3*4 + 4*5) = 2(15 + 12 + 20) = 2(47) = 94 cm²

Volume = 5 * 3 * 4 = 60 cm³

2. A cuboid has a volume of 240 cm³ and its length is 8 cm. If the width is 5 cm, find its height.

Volume = length × width × height

240 = 8 × 5 × height

height = 240 / (8 * 5) = 6 cm

Study Guide

When studying cuboids, it's important to understand the characteristics of a cuboid, such as its faces, edges, and vertices. You should also become familiar with the formulas for calculating the surface area and volume of a cuboid. Practice solving problems involving cuboids to reinforce your understanding of the concepts.

Remember, the surface area of a cuboid is the sum of the areas of its 6 faces, and the volume is the product of its length, width, and height. With enough practice, you'll become comfortable working with cuboids and be able to solve problems with confidence.