## Book: RS Aggarwal - Mathematics

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

#### Subject: Maths - Class 10th

##### Q. No. 6 of Exercise 18B

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

6
##### The length of a chain used as the boundary of a semicircular park is 108 m. Find the area of the park.

In this question the length of chain used as boundary of the semicircular park is the perimeter of the semicircular park. By using this we will first calculate the radius of the semicircular park and then area of semicircle consequently.

Length of chain = 108 m

Length of chain = Perimeter or circumference of semicircle

Therefore, Circumference or Perimeter of semicircle = 108 m

Also, Circumference or Perimeter of semicircle = πr

Where r = radius of semicircle

πr = 108

(put π = 22/7)

On rearranging,

r = 34.46 m

Therefore, radius of semicircle is 34.36 m

As, Area of semicircle

Put value of ‘r’ in equation 1, we get

Area of semicircle

(put π = 22/7)

On rearranging,

= 1855.63 m2

The area of the semicircular park is 1855.63 m2.

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