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, focuses on the fundamental concepts of constructing geometric figures. The NCERT Solutions provide step-by-step guidance on drawing circles with specific radii, constructing concentric circles, and understanding the properties of shapes formed by joining the ends of diameters. It covers drawing a circle, marking points in the interior and exterior, and identifying figures like rectangles and squares when diameters are perpendicular. These solutions are designed to help students visualize and accurately construct geometric shapes, reinforcing their understanding of basic geometry. They are an excellent resource for exam preparation, offering clear explanations and visual aids to master practical geometry skills.

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BoardCBSE
ClassClass 6
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 14: Practical Geometry

Chapter summary

Chapter 14, Practical Geometry, for Class 6 Mathematics, introduces students to the basics of geometric constructions. The NCERT Solutions cover drawing circles of given radii, constructing concentric circles, and exploring the shapes formed by diameters. Students will learn to identify rectangles and squares based on the properties of their diagonals (diameters) and practice marking points relative to a circle's interior and exterior. This chapter builds foundational skills for more complex geometric drawing and understanding.

Learning outcomes

  • Understand the concept of a circle's radius and diameter.
  • 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 perpendicular diameters.
  • Distinguish between points located inside, on, and outside a circle.

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
  • Properties of rectangles
  • Properties of squares
  • Points inside and outside a circle
  • Geometric constructions

Important topics

  • Drawing circles with a given radius
  • Constructing concentric circles
  • Identifying shapes formed by perpendicular diameters (Square)
  • Identifying shapes formed by any two diameters (Rectangle)
  • Points relative to a circle (interior, exterior, on the circle)

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Questions and Solutions

Question 1

Draw a circle of radius 3.2 cm.
Solution:

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

  1. Take a compass and open it to a radius of 3.2 cm using a ruler.
  2. Mark a point on the paper where you want the center of the circle to be. Label this point 'O'.
  3. Place the sharp pointer of the compass on the center point 'O'.
  4. Carefully rotate the compass, keeping the pointer fixed at 'O', to draw the complete circle with the pencil end.

The resulting figure 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 the paper to serve as the common center for both circles.
  2. For the first circle, open the compass to a radius of 4 cm.
  3. Place the pointer of the compass on 'O' and rotate the pencil end to draw the first circle.
  4. For the second circle, adjust the compass to a radius of 2.5 cm.
  5. Place the pointer of the compass again on the same center 'O' and rotate the pencil end to draw the second circle.

You will now have two circles, one with a 4 cm radius and another with a 2.5 cm radius, both centered at '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, passing through the center 'O'.
  3. Join the endpoints of these diameters in order: A to C, C to B, B to D, and D to A.

The figure obtained is a rectangle. You can check this by measuring the sides and angles:

  • Measure the lengths of the opposite sides (e.g., AC and BD, CB and DA). They should be equal.
  • Measure the angles at each vertex (e.g., ∠ACB, ∠CBD, ∠BDA, ∠DAC). Each angle should measure 90 degrees.

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, say AB and CD, intersecting at 'O' at a 90° angle.
  3. Join the endpoints in order: A to C, C to B, B to D, and D to A.

The figure obtained is a square. You can verify this by measuring:

  • All four sides (AC, CB, BD, DA) should be equal in length.
  • Each angle at the vertices (∠ACB, ∠CBD, ∠BDA, ∠DAC) should measure 90 degrees.

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 the circle and mark the points:

  1. Choose a point on your paper to be the center of the circle and label it 'O'.
  2. Place the pointer of the compass on 'O' and rotate the pencil end to draw a circle. The distance from 'O' to any point on the drawn line is the radius.
  3. To mark point A (on the circle): Choose any point directly on the circumference (the line you just drew) and label it 'A'.
  4. To mark point B (in the interior of the circle): Choose any point inside the circle, not on the circumference, and label it 'B'. The distance of 'B' from 'O' will be less than the radius.
  5. To mark point C (in the exterior of the circle): Choose any point outside the circle, not on the circumference, and label it 'C'. The distance of 'C' from 'O' will be greater than the radius.

You will have point 'A' on the circle's boundary, point 'B' within the circle's area, and point 'C' outside the circle's area.

Common mistakes

  • Incorrectly opening the compass to the wrong radius.
  • Not placing the compass pointer precisely at the center point.
  • Confusing interior and exterior points of a circle.
  • Misidentifying shapes formed by diameters due to measurement errors.

Revision tips

  • Practice drawing circles with various radii to ensure accuracy.
  • Use a ruler to double-check the compass opening before drawing.
  • Clearly label all points and lines in your constructions.
  • Review the properties of rectangles and squares when working with diameters.

Practice MCQs

Q1. What is the primary tool used to draw a circle in practical geometry?

Q2. If two circles share the same center, they are called:

Q3. When the ends of two perpendicular diameters of a circle are joined, what figure is formed?

Q4. A point is in the exterior of a circle if its distance from the center is:

Q5. What shape is formed by joining the ends of any two diameters of a circle?

Frequently asked questions

What is the main focus of Chapter 14: Practical Geometry for Class 6 Maths?

Chapter 14 focuses on the practical skills of constructing basic geometric figures, primarily circles, and understanding the shapes formed by their diameters.

How do I draw a circle of a specific radius accurately?

To draw a circle of a specific radius, open the compass to that exact measurement using a ruler, place the compass pointer at the desired center point, and then rotate the pencil end to draw the circle.

What is the difference between a rectangle and a square formed by diameters?

When the ends of any two diameters are joined, a rectangle is formed. If these two diameters are perpendicular to each other, the resulting figure is a square.

What does it mean for a point to be in the interior or exterior of a circle?

A point is in the interior if it's inside the circle (distance from center < radius), and in the exterior if it's outside the circle (distance from center > radius).

Are these NCERT Solutions helpful for exam preparation?

Yes, these solutions provide clear, step-by-step guidance and explanations for all exercises, helping students understand the concepts and practice constructions for better exam performance.

Important links

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