Volume and Capacity

9.6 Volume and Capacity

Description

Quick Overview

This section explores the concepts of volume and capacity, highlighting their definitions and the relationship between them.

Standard

In this section, volume refers to the space occupied by an object, while capacity refers to the amount a container can hold. The relationship between cubic centimeters and liters is established, providing context for practical applications in measurement.

Detailed

Volume and Capacity

In this section, we define volume and capacity, explaining their essential differences and how they relate in practical applications. Volume is the space occupied by a three-dimensional object, while capacity refers to the amount a container can hold. For instance, a water tin holding 100 cm³ of water indicates a capacity of 100 cm³.

We also discuss the measurement relationship between different units: 1 mL = 1 cm³ and 1 L = 1000 cm³, leading to the larger equivalence of 1 m³ = 1,000,000 cm³ = 1000 L.

Two examples demonstrate these concepts in action, such as calculating the height of a cuboid and the capacity of a godown by dividing the volume by the volume of smaller boxes.

Key Concepts

  • Volume: Refers to the amount of space an object occupies.

  • Capacity: Refers to how much a container can hold.

  • Relationship between Volume and Capacity: 1 mL = 1 cm³ and 1 L = 1000 cm³.

Memory Aids

🎵 Rhymes Time

  • Volume measures space so wide, capacity counts what you can slide.

📖 Fascinating Stories

  • Imagine a jug that can hold 2 liters of water. The jug takes up space on the shelf (volume), and the amount of water it can hold (capacity) reminds us of how they work together.

🧠 Other Memory Gems

  • V = Volume, C = Capacity, M = Measure. Remember: Measure how much each can occupy!

🎯 Super Acronyms

VICs

  • Volume Indicates Capacity.

Examples

  • Example 8 illustrates how to find the height of a cuboid given its volume and base area.

  • Example 9 demonstrates calculating how many smaller boxes fit into a larger storage area by dividing volumes.

Glossary of Terms

  • Term: Volume

    Definition:

    The amount of space occupied by a three-dimensional object.

  • Term: Capacity

    Definition:

    The quantity that a container can hold, often measured in liters.

  • Term: Cubic Centimeter (cm³)

    Definition:

    A metric unit of volume equal to a cube measuring 1 cm on each side.

  • Term: Liter (L)

    Definition:

    A metric unit of capacity, equal to 1000 cm³.

  • Term: Meter Cubed (m³)

    Definition:

    A unit of volume in the metric system, equal to 1,000,000 cm³.