Grade 6
  1. Number System  1.1. Whole Numbers  1.1.1. Place Value and Face Value  1.1.2. Comparing and Ordering Numbers  1.1.3. Rounding Numbers  1.1.4. Properties of Whole Numbers (Associative, Commutative, Distributive)  1.2. Integers  1.2.1. Introduction to Integers  1.2.2. Addition and Subtraction of Integers  1.2.3. Multiplication and Division of Integers  1.2.4. Properties of Integer Operations  1.3. Fractions  1.3.1. Types of Fractions  1.3.2. Equivalent Fractions  1.3.3. Simplification of Fractions  1.3.4. Addition and Subtraction of Fractions  1.3.5. Multiplication and Division of Fractions  1.3.6. Comparing and Ordering Fractions  1.4. Decimals  1.4.1. Understanding Decimals  1.4.2. Conversion between Fractions and Decimals  1.4.3. Addition and Subtraction of Decimals  1.4.4. Multiplication and Division of Decimals  1.4.5. Comparing and Ordering Decimals
  2. Algebra  2.1. Basics of Algebra  2.1.1. Variables and Constants  2.1.2. Expressions and Equations  2.1.3. Algebraic Terms and Coefficients  2.2. Solving Simple Equations  2.2.1. Balancing Equations  2.2.2. Solving One-Step Equations  2.2.3. Solving Two-Step Equations  2.3. Patterns and Sequences  2.3.1. Identifying Patterns  2.3.2. Arithmetic Sequences
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Equivalent Ratios  3.1.3. Simplifying Ratios  3.2. Proportion  3.2.1. Introduction to Proportion  3.2.2. Direct and Inverse Proportions  3.3. Percentages  3.3.1. Converting Ratios to Percentages  3.3.2. Percentage Increase and Decrease  3.3.3. Discount and Profit Calculations  3.3.4. Simple Interest Calculations in Percentages in Ratio and Proportion
  4. Geometry  4.1. Basic Geometric Shapes  4.1.1. Points, Lines, and Angles  4.1.2. Types of Angles  4.1.3. Intersecting and Parallel Lines  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Properties of Triangles  4.2.3. Sum of Angles in a Triangle  4.2.4. Congruence of Triangles  4.3. Quadrilaterals  4.3.1. Types of Quadrilaterals  4.3.2. Properties of Quadrilaterals  4.4. Circles  4.4.1. Radius and Diameter  4.4.2. Circumference and Area  4.4.3. Arcs and Chords  4.4.4. Sector and Segment
  5. Mensuration  5.1. Perimeter  5.1.1. Perimeter of Simple Shapes  5.2. Area  5.2.1. Area of Rectangles and Squares  5.2.2. Area of Triangles and Parallelograms  5.2.3. Area of Composite Figures  5.2.4. Area of Trapezium  5.3. Volume  5.3.1. Volume of Cubes and Cuboids  5.3.2. Volume of Cylinders  5.3.3. Volume of Cones  5.3.4. Surface Area of Simple Solids
  6. Data Handling  6.1. Introduction to Data  6.1.1. Types of Data  6.1.2. Organizing Data  6.1.3. Frequency Distribution  6.2. Graphs and Charts  6.2.1. Bar Graphs  6.2.2. Line Graphs  6.2.3. Pictographs  6.2.4. Pie Charts  6.3. Mean, Median, and Mode  6.3.1. Calculating Mean  6.3.2. Finding Median  6.3.3. Identifying Mode  6.3.4. Range of Data in Mean, Median, and Mode
  7. Probability  7.1. Basics of Probability  7.1.1. Understanding Probability  7.1.2. Probability of Simple Events  7.1.3. Experimental and Theoretical Probability
  8. Practical Geometry  8.1. Construction of Shapes  8.1.1. Constructing Triangles  8.1.2. Constructing Quadrilaterals  8.1.3. Constructing Circles and Arcs  8.2. Symmetry  8.2.1. Line of Symmetry  8.2.2. Rotational Symmetry  8.2.3. Translational Symmetry

Grade 6 → Mensuration ↓


Volume


In math, especially when we're talking about shapes and objects, we often use the term "volume." Volume is a simple but essential concept used to understand how much space a solid object takes up. In simple terms, volume is the space an object occupies in three dimensions.

What is volume?

Volume is a quantity that represents the amount of space present within a three-dimensional object or shape. Unlike area, which only measures length and width (2D), volume also takes into account depth. Simply put, while area measures the space inside a shape like a rectangle or square, volume measures the space inside a three-dimensional object like a cube or box.

Units of volume

The standard units for measuring volume are cubic units. Some commonly used units are:

  • Cubic centimetre (cm 3)
  • Cubic metre (m 3)
  • The liter, often used for liquids.
  • Millilitres, another commonly used unit for liquids.

Volume of a cube

A cube is a three-dimensional shape with all sides the same length. To find the volume of a cube, you need to multiply the length of one side by itself three times. In other words, the volume of a cube is side × side × side.

    Volume of a cube = side × side × side

Suppose you have a cube whose each side is 3 cm. Its volume will be:

    Volume = 3 cm × 3 cm × 3 cm = 27 cm 3

Visual example of a cube

3 cm

Volume of a rectangular prism

A rectangular prism, also called a cuboid, is a shape that has different lengths for the width, height, and depth. To calculate the volume, multiply the length by the width and multiply the height by the length.

    Volume of rectangular prism = length × width × height

For example, suppose you have a box that is 4 cm long, 2 cm wide, and 3 cm high. The volume is calculated as follows:

    Volume = 4 cm × 2 cm × 3 cm = 24 cm 3

Visual example of a rectangular prism

4 cm 3 cm 2 cm

Volume of a cylinder

A cylinder is like a soup can, with two parallel circular bases connected by a curved surface. To find its volume, you take the area of one of the circular bases and multiply it by the height of the cylinder. The area of a circular base is found using the formula π × radius 2.

    Volume of cylinder = π × radius 2 × height

If you are given a cylinder with a base radius of 2 cm and a height of 5 cm, the volume will be calculated as follows:

    Volume = 3.14 × (2 cm × 2 cm) × 5 cm = 62.8 cm 3

Volume of a sphere

A sphere is a perfectly round three-dimensional object, such as a basketball or bubble. For spheres, the volume is calculated using a more complex formula, which involves multiplying four-thirds by π and the cube of the radius:

    Volume of sphere = (4/3) × π × radius 3

Consider a sphere of radius 3 cm. Its volume will be:

    Volume = (4/3) × 3.14 × (3 cm × 3 cm × 3 cm) = 113.04 cm 3

Text example

Let's consider another example where you have a swimming pool. The pool is rectangular, with a length of 10 m, a width of 5 m, and a depth of 2 m. To fill the pool with water, you will need to know its volume:

    Volume = 10 m × 5 m × 2 m = 100 m 3

This volume tells us how much water the pool will hold when it is filled to full capacity.

Finding volume in real life

Understanding volume is not just important for math classes, but it also plays an important role in everyday life. Here are some examples where we encounter the concept of volume:

  • Drinks: When you buy a bottle of soda, the label often says how much liquid it contains, usually measured in milliliters or liters.
  • Cooking: Baking recipes often call for specific amounts of ingredients, like one cup of milk or two teaspoons of vanilla extract.
  • Shipping: Companies use volume measurements to determine how much space is needed to ship different products.
  • Storage: Volume is essential in determining how much stuff storage boxes can hold.

Summary and conclusion

Volume is a fundamental mathematical concept that helps us measure the space occupied by three-dimensional objects. From cubes to spheres, each shape has its own way of calculating volume. Units such as cubic centimeters, meters, and liters enable us to measure and compare volume efficiently.

By understanding and applying the principles of volume, we can solve a variety of practical problems in everyday life. Whether it's determining how much liquid a cup can hold or calculating the amount of water needed for a swimming pool, volume helps us understand the physical world in a systematic way.

As you continue learning, always remember that volume is simply a measure of space — a powerful tool for measuring tangible aspects of the world around us.


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