NCERT Solutions for Class 6 Maths Chapter 8 - Playing with Constructions Exercise 8.1

Exercise 8.1

Question 1.

A Person

Draw a figure in the given form to depict “A person”. How will you draw this?

This figure has two components.

You might have figured out a way of drawing the first part. See this for drawing the second part.

The challenge here is to find out where to place the tip of the compass and the radius to be taken for drawing this curve. You can fix a radius in the compass and try placing the tip of the compass in different locations to see which point works for getting the curve. Use your estimate to determine where to keep the tip.

Ans:

Step 1. We start with the base of the diagram. We take a line AB of length 4 cm as the base. (Fig. 1)

Step 2. At A and B, draw perpendicular lines using a protractor. (Fig. 2)

Step 3. Using a ruler, mark points C and D such that AC = 4 cm and BD = 4 cm. Join C and D by a line. (Fig. 3)

Step 4. Using a ruler, take point M on the CD such that CM = 2 cm. M is the midpoint of CD. Using a protractor, draw a perpendicular to CD at M. Take a point P on this perpendicular such that PM = 2 cm. Distance PM can also be slightly less than or greater than 2 cm. (Fig. 4)

Step 5. Join PD. With centre at P, draw an arc from D to C of a radius equal to PD. With centre at P, draw a circle of radius 1.5 cm. Extend PM to touch the arc. (Fig. 5)

Step 6. Erase the extra lines in Fig. 5 as in Fig. 6.

Step 7. Fig. 6 represents the required depiction of the given “A person”.

Construct this.

As the length of the central line is not specified, we can take it to be of any length. Let us take AB to be the central line such that the length of AB is 8 cm. We write this as

AB = 8 cm. Here, the first wave is drawn as a half circle.

1. What radius should be taken in the compass to get this half circle? What should be the length of AX? 

Ans:  We have AB = 8 cm.

Since the “Wavy Wave” has two equal half circles, we have AX = XB.

∴ X is the mid-point of AB.

∴ AX = $\frac{8}{2}= 4 cm$

∴ The length of AX is 4 cm.

Let M be the mid-point of AX.

∴ AM = MX =  $\frac{8}{2}= 4 cm$

The centre of the half circle is M.

∴ Radius of half circle = AM = 2 cm

∴ The radius of the half circle is 2 cm.

2. Take a central line of a different length and try to draw the wave on it. 

Ans: Step 1. We start with the central line of different lengths, say, 10 cm. (Figure 1)

Step 2. Since 

10 ÷ 2 = 5, using a ruler, take point C on AB such that AC = 5 cm. C is the mid-point of AB.

As 5 ÷ 2 = 2.5, using a ruler, take points D on AC and E on CB such that AD = 2.5 cm and CE = 2.5 cm.

D is the mid-point of AC and E is the mid-point of CB. (Figure 2)

Step 3. With centre at D, draw a half circle above the central line AB and of radius 2.5 cm. With centre at E, draw a half circle below the central line AB and of radius 2.5 cm. (Figure 3)

Step 4. Draw vertical lines in the half circles above and below the line AB. (Figure 4)

Step 5. The figure represents the required depiction of the given “Wavy Wave” with the central line of length 10 cm.

Question 3.

Eyes

How do you draw these eyes with a compass?

Draw a figure in the given form to depict “Eyes”.

Solution:

Step 1. Take a line AB of length 8.5 cm (4 cm + 0.5 cm + 4 cm) as a base. Take points C and D on AB such that AC = 4 cm and AD = 4.5 cm (4 cm + 0.5 cm). (Fig. 1)

Step 2. Take points E and F on AB such that AE = 2 cm and FB = 2 cm. E is the mid-point of AC and F is the mid-point of DB. (Fig. 2)

Step 3. Using a protractor, draw perpendiculars at E and F. (Fig. 3)

Step 4. Using a ruler, take points G, H, I, and J such that EG, EH, FI, and FJ are all equal to 1.5 cm. Equal distances can also be slightly less than or greater than 1.5 cm (Fig. 4)

Step 5. With the centre at G, draw an arc from A to C of a radius equal to AG. Similarly, with the centre at H, I, and J draw arcs of radius equal to AG. Erase the extra lines as shown in Fig. 5.

Step 6. At points E and F, draw two black dots of big size. (Fig. 6)

Step. 7. Figure represents the required depiction of “Eyes”.

Benefits of NCERT Solutions for Class 6 Maths Chapter 8 Exercise 8.1 Playing with Constructions

• The solutions provide detailed explanations of geometric constructions, helping students grasp the fundamental concepts clearly.

• Each construction problem is presented with step-by-step instructions, making it easier for students to follow and replicate the processes.

• By practising geometric constructions, students develop practical skills in using a compass and ruler, which are essential tools in geometry.

• The solutions are aligned with the CBSE Class 6 Maths syllabus, ensuring that all necessary topics related to constructions are covered comprehensively.

• Regular practice with these solutions enhances students’ ability to approach and solve geometric problems effectively.

• Engaging with constructions fosters spatial reasoning and visualisation skills, which are important in mathematics and real-life applications.

Class 6 Maths Chapter 8: Exercises Breakdown

Important Study Material Links for Class 6 Maths Chapter 8 - Playing with Constructions

Conclusion

The NCERT Solutions for Class 6 Maths Chapter 8 Exercise 8.1, Playing with Constructions, are an invaluable resource for students seeking to master geometric constructions. With clear, step-by-step guidance and practical applications, these solutions enhance understanding and confidence in using essential tools like a compass and ruler. Aligned with the CBSE syllabus, they provide comprehensive coverage of the necessary concepts, preparing students for more advanced topics in geometry. The availability of FREE PDF downloads ensures easy access for effective study and revision. Overall, these solutions empower students to develop strong foundational skills in geometry, paving the way for future mathematical success.

Chapter-Specific NCERT Solutions for Class 6 Maths

The chapter-wise NCERT Solutions for Class 6 Maths are given below. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

Related Important Links for Maths Class 6

Along with this, students can also download additional study materials provided by Vedantu for Maths Class 6.