Exercise 4.2 (Construction of circles and concentric circles)

Exercise 4.2

1. Draw circles for the following measurements of radius (r)/ diameters(d).

(i) r = 4 cm

(ii) d = 12 cm

(iii) r = 3.5 cm

(iv) r = 6.5 cm.

(v) d = 6 cm

Solution:  

(i) r = 4cm

Step 1 : Market a point ‘O’ on the paper.

Step 2 : Extended the compass distance equal to radius 4 cm.

Step 3 : At center ‘O’, helded the compass firmly and placed the pointed end of the compass.

Step 4 : Slowly rotated the compass around to get the circle.

(ii) d =12cm

given d = 12 cm

∴ radius r = d/2 = 12/2 = 6 cm

Step 1 : Market a point ‘O’ on the paper.

Step 2 : Extended the compass distance equal to radius 6 cm.

Step 3 : At center ‘O’, held the compass firmly and placed the pointed end of the compass.

Step 4 : Slowly rotated the compass around to get the circle.

(iii) r = 3.5cm

Step 1 : Market a point ‘O’ on the paper.

Step 2 : Extended the compass distance equal to radius 3.5 cm.

Step 3 : At center ‘O’, held the compass firmly and placed the pointed end of the compass.

Step 4 : Slowly rotated the compass around to get the circle.

(iv) r = 6.5 cm

Step 1 : Market a point ‘O’ on the paper.

Step 2 : Extended the compass distance equal to radius 6.5 cm.

Step 3 : At center ‘O’, held the compass firmly and placed the pointed end of the compass.

Step 4 : Slowly rotated the compass around to get the circle.

(v) d = 6 cm

∴ radius r = d / 2 = 6 / 2 = 3 cm

Step 1 : Market a point ‘O’ on the paper.

Step 2 : Extended the compass distance equal to radius 3 cm.

Step 3 : At center ‘O’, held the compass firmly and placed the pointed end of the compass.

Step 4 : Slowly rotated the compass around to get the circle.

2. Draw concentric circles for the following measurements of radii / diameters. Find out the width of each circular ring.

(i) r = 3 cm and r = 5 cm.

(ii) r = 3.5 cm and r = 6.5 cm.

(iii) d = 6.4 cm and d = 11.6 cm.

(iv) r = 5 cm and r = 7.5 cm.

(v) d = 6.2 cm and r = 6.2 cm.

(vi) r = 7.1 cm and d = 12 cm.

Solution: 

(i) r = 3 cm and r = 5 cm

Width of the circular ring = OB – OA = 5 – 3 = 2 cm

Step 1 : Drawn a rough diagram and market the given measurements

Step 2 : Taken any point O and marked it as the center.

Step 3 : With O as center drawn a circle of radius OA = 3 cm.

Step 4 : With O as center drawn a circle of radius OB = 5 cm. Thus the concentric circles C₁ and C₂ are drawn.

Width of the circular ring = OB – OA = 5 –3 = 2 cm

(ii) r = 3.5 cm and r = 6.5 cm

Step 1 : Drawn a rough diagram and market the given measurements

Step 2 : Taken any point O and marked it as the center.

Step 3 : With O as center drawn a circle of radius OA = 3.5 cm.

Step 4 : With O as center drawn a circle of radius OB = 6.5 cm. Thus the concentric circles C₁ and C₂ are drawn.

Width of the circular ring = OB – OA = 6.5 –3.5 = 3 cm

 (iii) d = 6.4 cm and d = 11.6 cm.

r = d / 2

∴ r = 6.4 / 2 = 3.2 cm   ;    r = 11.6 / 2 = 5.8 cm

Step 1 : Drawn a rough diagram and market the given measurements

Step 2 : Taken any point O and marked it as the center.

Step 3 : With O as center drawn a circle of radius OA = 3.2 cm.

Step 4 : With O as center and drawn a circle of radius OB = 5.8 cm. Thus the concentric circles C₁and C₂ are drawn.

Width of the circular ring = OB – OA = 5.8 – 3.2 = 2.6 cm

(iv) r = 5 cm and r = 7.5 cm.

Step 1 : Drawn a rough diagram and market the given measurements

Step 2 : Taken any point O and marked it as the center.

Step 3 : With O as center drawn a circle of radius OA = 5 cm.

Step 4 : With O as center drawn a circle of radius OB = 7.5 cm. Thus the concentric circles C₁ and C₂ are drawn.

Width of the circular ring = OB – OA = 7.5 – 5 = 2.5 cm

(v) d = 6.2 cm and r = 6.2 cm.

 r = d/2

∴ r = 6.2 / 2 = 3.1 cm and r = 6.2 cm

Step 1 : Drawn a rough diagram and market the given measurements

Step 2 : Taken any point O and marked it as the center.

Step 3 : With O as center, drawn a circle of radius OA =3.1 cm.

Step 4 : With O as center, drawn a circle of radius OB = 6.2 cm. Thus concentric circles C₁ and C₂ are drawn.

Width of the circular ring = OB – OA = 6.2 – 3.1 = 3.1 cm

(vi) r = 7.1 cm and d = 12 cm.

 r = d/2

 ∴ r = 12/2 = 6 cm and r = 7.1 cm

Step 1 : Drawn a rough diagram and marked the given measurements

Step 2 : Taken any point O and marked it as center.

Step 3 : With O as center, drawn a circle of radius OA = 6 cm.

Step 4 : With O as center, drawn a circle of radius OB = 7.1 cm. Thus concentric circles C₁ and C₂ are drawn.

Width of the circular ring = OB – OA = 7.1 – 6 = 1.1 cm