Question

A path of 4 m width runs round a semi circular grassy plot whose circumference is 163 3/7 m find the area of the path

Question is from cbse 10 rd sharma topic area related to circles

Answer 1

 its 163  3/7 as in mixed fraction  than improper fraction is  1144 / 7

now circumference = 1144 / 7

= 2 * pi * r = 1144 /7 

=2 * 22 / 7 * r = 1144 /7 

now 7 will cancel out from both side because when we take 7 from  LHS to RHS it will divided out......

now    r = 26

 

now since path is 4m wide than outer radii = 30

 

now area of path = area of outer circle( with path) - area of inner circle (without path)

                           =   pi * 30 *30 - pi * 26 * 26

                           =  pi( 900 - 676 )

                          =  22 * 224 / 7

                       =    22 * 32

therefore area of path =  704 m2

i hope it helps

Answer 2

Answer:

Step-by-step explanation:

Circumference of plot=163  

7

3

​  

m=  

7

1144

​  

m

⇒2πr=  

7

1144

​  

⇒r=  

7×44

1144×7

​  

=26m

i) Area of path=π(R  

2

−r  

2

)

=  

7

22

​  

((26+4)  

2

−(26)  

2

)

=  

7

22

​  

×14.97=47.05㎡

ii) Cost of graveling=Rs. (47.05×1.50)=Rs. 70.575

iii) Area of plot=πr  

2

=  

7

22

​  

×26×26=2124.57㎡

Cost of turfing=Rs. (2124.57×0.45)=Rs. 956.06