Cuboid

9.4.1 Cuboid

Description

Quick Overview

This section discusses the surface area of a cuboid, including its calculation and key properties.

Standard

In this section, we learn about the total surface area of a cuboid, derived formulae, and lateral surface area. We also see practical examples illustrating these concepts.

Detailed

Detailed Summary

In this section, we explore the concept of the cuboid, which is a three-dimensional geometric figure outlined by six rectangular faces. The total surface area of a cuboid is essential for various real-world applications, like packaging and construction. The formula for calculating the total surface area (SA) is:

Total Surface Area of a Cuboid:

SA = 2(lb + bh + hl)
Where:
- l = length
- b = breadth (width)
- h = height

This formula indicates that there are three pairs of identical rectangles in a cuboid. The area of each rectangular face needs to be calculated and summed to find the total surface area.

In addition, we also discuss lateral surface area (the area excluding the base and top) which is given by:
Lateral Surface Area = 2h(l + b).

We delve into a practical example: if a cuboid has dimensions of 20 cm (height), 15 cm (length), and 10 cm (width), the total surface area would be calculated as:
- SA = 2(20 × 15 + 20 × 10 + 10 × 15) = 1300 cm².

This section prepares the learners to understand and apply the concept of surface area to various cuboid-related problems.

Key Concepts

  • Total Surface Area: Calculation of all external surfaces of a cuboid.

  • Lateral Surface Area: Area of sides only about the base and top.

  • Dimensions: Measurements that define the size of a cuboid.

Memory Aids

🎵 Rhymes Time

  • For a cuboid tall and wide, add all six sides, it’s a ride!

📖 Fascinating Stories

  • Imagine a box storing secrets, each side needs painting; to know how much, we add all its faces!

🧠 Other Memory Gems

  • For 'SURFACE AREA', remember: 'Six' sides - 'Unique' pairs.

🎯 Super Acronyms

LWH - Length, Width, Height; use these for calculations right!

Examples

  • Example 1: For a cuboid with length = 5 cm, width = 3 cm, and height = 4 cm, the total surface area is 2(53 + 34 + 5*4) = 94 cm².

  • Example 2: Lateral surface area for the same cuboid would be 24(5 + 3) = 64 cm².

Glossary of Terms

  • Term: Cuboid

    Definition:

    A three-dimensional figure with six rectangular faces.

  • Term: Surface Area

    Definition:

    The total area that the surface of an object occupies.

  • Term: Lateral Surface Area

    Definition:

    The area of the sides of a three-dimensional object.

  • Term: Dimensions

    Definition:

    Measurements of length, width, and height.