Cube

9.5.2 Cube

Description

Quick Overview

This section presents the definition and volume formula of a cube, explaining its significance as a special type of cuboid.

Standard

In this section, we learn that a cube is a specific kind of cuboid with equal sides, and its volume can be calculated using the formula V = l³, where l is the length of a side. This formula highlights the significance of cubes in measuring volume in a three-dimensional space.

Detailed

Cube

A cube is a three-dimensional geometric figure that has all its sides of equal length. Each face of a cube is a square, and because of this unique property, a cube can be viewed as a specific type of cuboid. In this section, we discuss how to calculate the volume of a cube, denoted by the formula V = l³, where "l" represents the length of one side. This formula is pivotal in learning how to understand and apply concepts of volume measurement for solid shapes in practical contexts. Calculating the volume of a cube is straightforward—simply multiplying the length of one side by itself twice (l × l × l). The importance of understanding how to compute the volume of a cube extends to various real-life applications, such as in architecture, packaging, and many areas of science and engineering.

Key Concepts

  • Cube: A three-dimensional shape with all equal sides.

  • Volume: Measure of how much space a solid occupies, calculated as l³ for cubes.

  • Cuboid: A more general term for three-dimensional rectangular shapes, which includes cubes.

Memory Aids

🎵 Rhymes Time

  • A cube's volume is easy, you know, just take the side and let it grow. Length times length times length is the flow!

📖 Fascinating Stories

  • Imagine stacking blocks—a cube is like a box, where every side fits snugly together, just as all the blocks fit perfectly.

🧠 Other Memory Gems

  • Remember 'Cubic Length' to calculate the volume of a cube: Length × Length × Length.

🎯 Super Acronyms

CUBE = Calculating Under Basic Equations (used for volume V = l³).

Examples

  • Example: Calculate the volume of a cube with a side of 4 cm. Solution: 4 × 4 × 4 = 64 cm³.

  • Example: Calculate the volume of a cube with a side of 1.5 m. Solution: 1.5 × 1.5 × 1.5 = 3.375 m³.

Glossary of Terms

  • Term: Cube

    Definition:

    A three-dimensional shape with six equal square faces.

  • Term: Volume

    Definition:

    The amount of three-dimensional space an object occupies.

  • Term: Cuboid

    Definition:

    A three-dimensional shape with rectangular faces.