CBSE Class 6 Mathematics Chapter 14: Practical Geometry NCERT Solutions

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NCERT Solutions PDF Class 6 PDF

This chapter, Practical Geometry, for CBSE Class 6 Mathematics, introduces fundamental concepts of drawing and understanding geometric shapes. The NCERT Solutions provide step-by-step guidance on constructing circles with specific radii, drawing concentric circles, and understanding the properties of figures formed by joining the ends of diameters. It covers how to identify points inside, outside, and on the circle. These solutions are designed to help students visualize and accurately perform geometric constructions, reinforcing their understanding of basic shapes and their characteristics. Practicing these exercises will build a strong foundation for more complex geometry in the future and aid in exam preparation by ensuring clarity on construction techniques.

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Quick info

BoardCBSE
ClassClass 6
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 14

Chapter summary

Chapter 14, Practical Geometry, focuses on the basic construction of circles and related figures. The NCERT Solutions cover drawing circles of given radii, constructing concentric circles, and exploring the shapes formed by joining the endpoints of diameters, including rectangles and squares. It also guides students in locating points relative to a circle (interior, exterior, on the circle). These solutions offer clear, actionable steps for each exercise, ensuring students can replicate the constructions accurately.

Learning outcomes

  • Understand the concept of a circle and its radius.
  • Learn to construct a circle using a compass with a given radius.
  • Construct concentric circles with the same center but different radii.
  • Identify and construct rectangles and squares by joining the ends of diameters.
  • Distinguish between points located inside, outside, and on the circumference of a circle.
  • Develop practical skills in geometric drawing and measurement.

Topics covered

Paper topics

  • Introduction to Practical Geometry
  • Drawing a circle with a given radius
  • Drawing concentric circles
  • Understanding diameters
  • Identifying shapes formed by diameters (rectangle, square)
  • Points in the interior of a circle
  • Points on the circle
  • Points in the exterior of a circle
  • Geometric constructions

Important topics

  • Construction of a circle
  • Concentric circles
  • Properties of shapes formed by diameters
  • Locating points relative to a circle

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Questions and Solutions

Question 1

Draw a circle of radius 3.2 cm.
Solution:

To construct a circle with a radius of 3.2 cm, follow these steps:

  1. Take a compass and adjust its width so that the distance between the pointer and the pencil tip is exactly 3.2 cm. You can use a ruler to measure this distance accurately.
  2. Choose a point on your paper where you want the center of the circle to be. Mark this point clearly with a sharp pencil and label it as 'O'.
  3. Place the metal pointer of the compass firmly on the center point 'O'.
  4. Keeping the pointer fixed on 'O', carefully rotate the compass by turning the pencil end slowly and steadily. Ensure the pencil maintains a consistent distance from the pointer (3.2 cm) throughout the rotation.
  5. Continue rotating until a complete circle is formed.

The figure drawn is the required circle with a radius of 3.2 cm.

Question 2

With the same centre O, draw two circles of radii 4 cm and 2.5 cm.
Solution:

To draw two circles with the same center 'O' but different radii, follow these steps:

  1. Mark a point 'O' on your paper to serve as the common center for both circles.
  2. For the first circle: Adjust the compass to a radius of 4 cm. Place the pointer of the compass on 'O' and rotate the pencil to draw the first circle.
  3. For the second circle: Now, adjust the compass to a radius of 2.5 cm.
  4. Place the pointer of the compass on the same center point 'O'.
  5. Rotate the pencil end slowly to draw the second circle around the same center.

You will now have two circles, one with a 4 cm radius and another with a 2.5 cm radius, both originating from the same center 'O'.

Question 3

Draw a circle and any two of its diameters. If you join the ends of these diameters, what is the figure obtained if the diameters are perpendicular to each other? How do you check your answer?
Solution:

Part 1: Joining the ends of any two diameters

  1. Draw a circle with center 'O'.
  2. Draw any two diameters, say AB and CD. A diameter passes through the center and has its endpoints on the circle.
  3. Join the endpoints of these diameters in order: A to C, C to B, B to D, and D to A.
  4. The figure obtained by joining the ends of any two diameters is a rectangle.

Checking the answer:

To verify that the figure is a rectangle, you can measure its sides and angles:

  • Measure the lengths of the opposite sides (e.g., AC and BD, CB and DA). You will find that opposite sides are equal in length.
  • Measure the angles at each vertex (A, C, B, D). You will find that each angle is 90 degrees. These properties confirm that the figure is a rectangle.

Part 2: Joining the ends of two perpendicular diameters

  1. Draw a circle with center 'O'.
  2. Draw two diameters that are perpendicular to each other. For example, draw diameter AB horizontally through the center, and diameter CD vertically through the center.
  3. Join the endpoints of these perpendicular diameters in order: A to C, C to B, B to D, and D to A.
  4. The figure obtained is a square.

Checking the answer:

To verify that the figure is a square:

  • Measure the lengths of all four sides (AC, CB, BD, DA). You will find that all four sides are equal in length.
  • Measure the angles at each vertex (A, C, B, D). You will find that each angle is 90 degrees. These properties confirm that the figure is a square.

Question 4

Draw any circle and mark points A, B and C such that: (a) A is on the circle. (b) B is in the interior of the circle. (c) C is in the exterior of the circle.
Solution:

Follow these steps to draw a circle and mark the points as required:

  1. Choose a point on your paper to be the center of the circle. Mark it and label it 'O'.
  2. Place the pointer of your compass on 'O' and rotate the pencil end to draw a circle. The size of the circle (its radius) can be any convenient length.
  3. To mark point A (on the circle): Choose any location directly on the boundary line of the circle you just drew. Mark this point and label it 'A'.
  4. To mark point B (in the interior of the circle): Choose any location within the boundary of the circle, but not on the boundary line itself. Mark this point and label it 'B'. This point is inside the circle.
  5. To mark point C (in the exterior of the circle): Choose any location outside the boundary line of the circle. Mark this point and label it 'C'. This point is outside the circle.

After completing these steps, you will have a circle with point A on its circumference, point B in its interior, and point C in its exterior.

Common mistakes

  • Incorrectly setting the compass width for the specified radius.
  • Not placing the compass pointer precisely at the center point.
  • Joining the ends of diameters without ensuring they are perpendicular when a square is expected.
  • Misidentifying points as being inside or outside the circle when they are on the circumference.

Revision tips

  • Practice drawing circles with various radii to ensure accuracy with the compass.
  • Carefully label all points and lines in your constructions.
  • Review the properties of rectangles and squares when constructing them from diameters.
  • Use a ruler to double-check measurements after drawing figures.

Practice MCQs

Q1. What is the first step in drawing a circle with a specific radius?

Q2. Concentric circles share the same:

Q3. If the two diameters used to form a quadrilateral are perpendicular, what shape is formed?

Q4. A point located 'in the interior of the circle' is:

Q5. What tool is primarily used for drawing circles in practical geometry?

Frequently asked questions

What is Chapter 14 of Class 6 Maths about?

Chapter 14, Practical Geometry, focuses on the basic skills of drawing circles and understanding geometric figures related to them, such as rectangles and squares formed by diameters.

How do I draw a circle of radius 3.2 cm?

To draw a circle of radius 3.2 cm, first open your compass to a width of 3.2 cm. Then, place the compass pointer at the desired center point and rotate the pencil end to draw the circle.

What are concentric circles?

Concentric circles are circles that share the same center point but have different radii, meaning they have different sizes.

What figure is formed if the ends of two perpendicular diameters are joined?

If the ends of two perpendicular diameters of a circle are joined, the figure obtained is a square.

How can I check if a point is inside, outside, or on the circle?

A point is inside if its distance from the center is less than the radius, on the circle if its distance equals the radius, and outside if its distance from the center is greater than the radius.

Are these solutions helpful for exam preparation?

Yes, these solutions provide clear, step-by-step methods for geometric constructions, helping students understand concepts and practice techniques essential for exams.

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