7th Maths : Term 2 Unit 2 : Measurements : Circumference of a Circle : Exercise 2.1 : Text Book Back Exercises Questions with Answers, Solution

**Exercise
2.1**

** **

**1.
Find the missing values in the following table for the circles with radius ( r),
diameter (d) and Circumference (C).**

**i) Radius r = 15 cm
**

Diameter d = 2r = 2 × l5 = 30cm

Circumference C = 2πr

= 2 × 22/7 × 15 cm = 660/7cm

= 94.28 cm

**ii) Circumference C
= 1760 cm**

2πr = 1760

2 × 22/7 × r = 1760

r = 1760×7 / 2×22 = 280 cm

Diameter d = 2r = 2 × 280 = 560 cm

**iii) Diameter d =
24 m**

radius r = d/2 = 24/2 = 12 m

Circumference C= 2πr

= 2 × 22/7 × 12 cm

= 528 / 7 = 75.42 m

** **

**2.
Diameters of different circles are given below. Find their circumference (Take ***π*** ****=**** 22/7).
**

**(i)
d = 70 cm**

Diameter d = 70 cm

Circumference C= πd

= 22/7 × 70 = 220 cm

Circumference = 220 cm

**(ii)
d = 56 m**

Diameter d= 56 cm

Circumference C = πd

= 22/7 × 56 m = 176 m

Circumference = 176 m

**(iii)
d = 28 mm **

Diameter d = 28 mm

Circumference C= πd

= 22/7 × 28 mm = 88 mm

Circumference = 88mm

** **

**3.
Find the circumference of the circles whose radii are given below.**

**(i)
49 cm**

Radius r = 49 cm

Circumference C = 2πr

= 2 × 22/7 × 49 = 308 cm

Circumference = 308 cm

**(ii)
91 mm**

Radius r = 91 mm

Circumference C = 2πr

= 2 × 22/7 × 91 mm = 572 mm

Circumference = 572 mm

** **

**4.
The diameter of a circular well is 4.2 m. What is its circumference?**

The diameter of a circular well d = 4.2 m

Radius r = d/2 = 42/2 = 2.1m

Circumference C = 2πr

= 2 × 22/7 × 2.1 =13.2 m

Circumference of a circular well = 13.2 m

** **

**5. The diameter of the bullock cart wheel
is 1.4 m. Find the distance covered by it in 150 rotations?**

The diameter of the bullock cart d = 1.4 m

radius r = d/2 = 14/2 = 0.7m

Circumference C = 2πr

= 2 × 22/7 × 0.7m = 4.4m

The distance covered in 1 rotation = 4.4 m

The distance covered in 150 rotation = 4.4 m × 150 = 660m

The distance covered in 150 rotation = 660 m

** **

**6. A ground is in the form of a circle
whose diameter is 350 m. An athlete makes 4 revolutions. Find the distance
covered by the athlete.**

Diameter of the ground d = 350 m

radius r = d/2 = 350/2 = 175 m

Circumference C = 2πr

= 2 × 22/7 × 175 m = 1100 m

Distance covered in 1 revolution = 1100 m

Distance covered in 4 revolution = 1100 × 4m = 4400 m

The distance covered by the athlete = 4400 m.

** **

**7. A wire of length 1320 cm is
made into circular frames of radius 7 cm each. How many frames can be made?**

The radius ofthe circular frame r = 7cm

Circumference C = 2πr

= 2 × 22/7 × 7 cm = 44 cm

The Length of the wire = 1320 cm

The Circumference of the frame = 44 cm

Number of Circular frames made = Length of the wire /
Circumference of the frame

= 1320 / ~~44~~ = 30.

Number of Circular frames made = 30.

** **

**8.
A Rose garden is in the form of circle of radius 63 m. The gardener wants
to fence it at the rate of ₹150 per metre. Find the cost of fencing?**

Radius of the rose garden r = 63 m

Circumference C = 2πr

= 2 × 22/7 × 63 m

Circumference of the rose garden = 396 m

The cost of fencing 1 metre = ₹ 150

The cost of fencing 396 metre = 396 × ₹ 150

The cost of fencing = ₹ 59,400

** **

__Objective type questions__

**9.
Formula used to find the circumference of a circle is**

(i) 2 πr *units*

(ii) πr^{2} + 2*r* *units *

(iii) πr^{2} *sq.
units*

(iv) πr^{3} *cu.
units*

*Answer :* (i) 22πr units

**10.
In the formula, C = 2πr , ‘r’ refers to **

(i) circumference

(ii) area

(iii) rotation

(iv) radius

*Answer :* (iv) radius

**11.
If the circumference of a circle is 82π, then the value of ‘r’ is **

(i) 41 *cm*

(ii) 82* cm*

(iii) 21 *cm*

* *(iv)
20 *cm*

*Answer :* (i) 41 cm

**12.
Circumfernce of a circle is always**

(i) three times its diameter

(ii) more than three times of its
diameter

(iii) less than three times of its
diameter

(iv) three times of its radius

*Answer :* (i) three times of its diameter

__ANSWERS:__

**Exercise 2.1 **

1. (i) d = 30 *cm*; c = 94.28* cm *(ii) *r* = 280 *cm*; d = 560* cm *(iii) *r* = 12 m; c =
75.42* m *

2. (i) 220* cm *(ii) 176* m *(iii) 88* m *

3. (i) 308* cm *(ii) 572* mm*

4. 13.2* m *

5. 660* m *

6. 4400* m *

7. 30 frames

8. ₹59,400

**Objective type questions **

9. (i) 2πr *units*

10. (iv) radius

11. (i) 41* cm *

12. (ii) more than three times of its diameter

Tags : Measurements | Term 2 Chapter 2 | 7th Maths , 7th Maths : Term 2 Unit 2 : Measurements

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7th Maths : Term 2 Unit 2 : Measurements : Exercise 2.1 (Circumference of a Circle) | Measurements | Term 2 Chapter 2 | 7th Maths

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