Cuboid

9.5.1 Cuboid

Description

Quick Overview

This section explores how to calculate the volume of a cuboid by using the formula volume = length × breadth × height.

Standard

The section discusses the concept of volume as the amount of space occupied by a three-dimensional object, specifically focusing on calculating the volume of a cuboid using the appropriate formula. It emphasizes understanding volume through practical examples and activities.

Detailed

Volume of Cuboid

The volume of a cuboid is the total space occupied by the cuboid, measured in cubic units. To find this volume, we use the straightforward formula: Volume = length × breadth × height (V = l × b × h). This formula stems from the relation of a cuboid to unit cubes, where the total volume equals the number of unit cubes that can fit within the given dimensions. In practical terms, when cubes (of equal size) are arranged to form a cuboid, the crucial measurements needed are the length, breadth, and height of the cuboid. Notably, the area of the base of the cuboid, calculated as length multiplied by breadth (l × b), is a key component in determining volume. The section provides practical activities to enhance understanding, such as measuring the volume of stacked papers, fostering a hands-on approach to learning this geometrical concept.

Key Concepts

  • Volume of a Cuboid: Measured using V = l × b × h.

  • Unit Cubes: The building blocks for measuring volume.

  • Base Area: Area of the base = l × b, which is intrinsic to finding volume.

Memory Aids

🎵 Rhymes Time

  • Cubes stack up, one by one; Officially measuring can be so much fun.

📖 Fascinating Stories

  • Imagine building a box with building blocks; you stack them high and wide to make a cuboid! Each block is a unit, and together they measure space.

🧠 Other Memory Gems

  • For volume, remember: 'Lettuce Before Hamburger' (Length × Breadth × Height).

🎯 Super Acronyms

V = LBH (Volume = Length x Breadth x Height).

Examples

  • If a cuboid has a length of 4 cm, breadth of 3 cm, and height of 2 cm, the volume is 4 × 3 × 2 = 24 cubic cm.

  • When stacking paper sheets with an area of 10 cm² and a height of 5 cm, the volume of the resulting cuboid is 10 × 5 = 50 cubic cm.

Glossary of Terms

  • Term: Volume

    Definition:

    The amount of space occupied by a three-dimensional object, measured in cubic units.

  • Term: Cuboid

    Definition:

    A three-dimensional shape with rectangular faces, defined by its length, breadth, and height.

  • Term: Cubic Unit

    Definition:

    A unit of measure for volume, defined as the space occupied by a cube with edges of one unit length.

  • Term: Base Area

    Definition:

    The area of the base of a three-dimensional shape, calculated as length times breadth.