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 → Practical Geometry → Construction of Shapes ↓


Constructing Circles and Arcs


In the world of geometry, shapes are fascinating, and circles and arcs hold their own special place. From car wheels to clock faces, circles are present everywhere in our daily lives. Understanding how to draw these shapes helps us understand their beauty and utility even more. Let's take a deeper look at the concepts of drawing circles and arcs in practical geometry.

What is a circle?

A circle is a perfectly round figure, where all points are the same distance from the center. This distance from the center to any point on the circle is called the radius.

Circumference of a circle

The total distance around the circle is called the circumference. We can calculate the circumference with the following formula:

C = 2πr

Here, r is the radius of the circle, and π (pi) is approximately 3.14.

Visual example: circle with center and radius

Centerradius

Constructing a circle

To draw a perfect circle, we use a tool called a compass. A compass has two arms - one with a sharp tip and the other with a pencil. The steps to draw a circle are as follows:

  1. Place the pointed tip of the compass on the paper. This point will be the center of the circle.
  2. Extend the other arm of the compass to the desired length of the radius.
  3. Keep the compass steady on the focal point and slowly rotate the pencil arm to draw the circle.

Example: Drawing a circle with radius 7 cm

Let's draw a circle with a radius of 7 cm. To do this:

  1. Set the compass so that the distance between the point and the pencil is 7 cm.
  2. Place the point on the paper where you want the center of the circle.
  3. Draw a circle of circumference 14 cm by rotating the compass steadily.

What is an arc?

An arc is a portion of a circle. Imagine cutting a slice of pie from the whole circle. The edge of that slice forms an arc. The arc represents a portion of the circumference and is defined by two end points.

Visual example: arc on a circle

Arch

Construction of the arch

A compass or protractor can be used to draw an arc. Here's how you can draw an arc with a compass:

  1. Draw the complete circle with the desired radius using the compass. This gives you guidelines for the arc.
  2. Decide the angle for the arc. For example, you might want an arc with a 60 degree angle.
  3. Using a protractor, mark the angle from one endpoint of the arc on the circumference of the circle.
  4. The part of the circle between the two marks is your arc.

Example: Drawing a 90 degree arc

To draw a 90 degree arc on a circle:

  1. Complete the circle using the compass with your chosen radius.
  2. Use the protractor to measure a 90 degree angle from a point on the circumference.
  3. Draw a line from the center to two points. The part of the circle between these lines is a 90 degree arc.

Real-world applications

Understanding circles and arcs is important in fields such as engineering, architecture, and art. Here are some examples of how they are applied:

  • Arches in buildings: The properties of arches are often used to distribute loads evenly.
  • Gears and wheels: Use the precision of circles for smooth rotation.
  • Design: Circles and arcs form the basis of many artistic designs and patterns.

Conclusion

Circles and arcs are fundamental shapes in geometry, playing a vital role in theoretical and practical applications. Mastering their construction prepares us for more advanced geometric challenges and demonstrates the mathematical precision inherent in the world around us.


Grade 6 → 8.1.3


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Constructing Quadrilaterals
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Constructing Circles and Arcs

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