## Book: RS Aggarwal - Mathematics

### Chapter: 18. Area of Circle, Sector and Segment

#### Subject: Maths - Class 10th

##### Q. No. 7 of Exercise 18B

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

7
##### The sum of the radii of two circles is 7 cm, and the difference of their circumferences is 8 cm. Find the circumferences of the circles.

Given Sum of the radius of the circles = 7 cm

the difference of their circumference = 8 cm

Let the radius one circle be ‘r1’ cm and other be ‘r2’ cm and circumference be ‘C1’ and ‘C2’ respectively.

Also, circumference of circle = 2πr

Where r = radius of the circle

C1 = 2πr1 and C2 = 2πr2

r1 + r2 = 7 eqn1

C1 – C2 = 8 eqn2

(Note: Her it is considered that r1>r2)

We can rewrite equation 2 as,

2πr1 – 2πr2 = 8

2π(r1 – r2) = 8

(taking 2π common from L.H.S)

Put the value of r1 from equation 3 in equation 1

(taking 11 as LCM on R.H.S)

Put value of r2 in equation 3

(from equation 3)

(taking 22 as LCM on R.H.S)

(by putting value of r1)

= 182/7

= 26 cm

(by putting value of r2)

= 126/7

= 18 cm

The circumference of circles are 26 cm and 18 cm.

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60