Cube

A cube is a three-dimensional shape that has six square faces, twelve edges, and eight vertices. All the sides of a cube are equal in length, and all the angles are right angles (90 degrees).

Formulas for a Cube

The formulas for a cube include:

• Surface Area: The total area of all the six faces of a cube. The formula for the surface area of a cube is 6a², where a is the length of the side.
• Volume: The amount of space inside the cube. The formula for the volume of a cube is a³, where a is the length of the side.
• Diagonal Length: The length of the space diagonal of the cube is a√3, where a is the length of the side.

Properties of a Cube

Some important properties of a cube include:

• All the faces of a cube are congruent squares.
• All the edges of a cube have the same length.
• All the angles between the faces are right angles (90 degrees).
• The diagonals of a face of a cube are equal in length and intersect at right angles.

Example Problems

Here are some example problems related to cubes:

1. If the side length of a cube is 5 cm, find its surface area and volume.
2. What is the length of the space diagonal of a cube with a side length of 3 inches?

Study Guide

To master the topic of cubes, make sure to understand the following concepts:

• Identifying the different parts of a cube (faces, edges, vertices).
• Understanding the formulas for surface area, volume, and diagonal length of a cube.
• Applying the properties of a cube to solve problems and real-life scenarios.