A path of 4m width runs rounda semi-circular grassy plot whose circumference is 163+3/7 m. find  

1. area of the path

2.cost of gravelling the path at the rate of Rs 1.50 per sq.m

3.cost of turfing the plot at the rate of 45 paise per sq.m

Asked by Divyaa | 27th Mar, 2017, 02:29: PM

Expert Answer:

Hi Divya,
 
There area two possibilities to for this diagram. If the diagram is given please post it. 
Otherwise based on the information given in the question, this will be the diagram. The answers however, are not matching your answer.Please check the solution and let us know if you have any doutbs regarding the solution.
begin mathsize 16px style 1. space Circumference space of space the space semi minus circular space plot equals space 163 3 over 7 space straight m equals 1144 over 7 space straight m
rightwards double arrow πr plus 2 straight r equals 1144 over 7
rightwards double arrow straight r open parentheses 22 over 7 plus 2 close parentheses equals 1144 over 7
rightwards double arrow straight r open parentheses 36 over 7 close parentheses equals 1144 over 7
rightwards double arrow straight r equals 31.8 space straight m space left parenthesis approximately right parenthesis
Radius space of space the space outer space semi minus circle equals straight r plus 4 equals 31.8 plus 4 equals 35.8 space straight m
So comma space area space of space the space path
equals area space of space the space big space semi short dash circle space bold minus space area space of space the space small space semi short dash circle
equals fraction numerator πR squared minus πr squared over denominator 2 end fraction
equals fraction numerator straight pi left parenthesis straight R squared minus straight r squared right parenthesis over denominator 2 end fraction
equals straight pi fraction numerator left parenthesis 35.8 squared minus 31.8 squared right parenthesis over denominator 2 end fraction
equals 22 over 7 fraction numerator left parenthesis 1281.64 minus 1011.24 right parenthesis over denominator 2 end fraction
equals fraction numerator 22 over denominator 7 cross times 2 end fraction left parenthesis 270.4 right parenthesis
almost equal to 425 space sq space straight m space left parenthesis approximately right parenthesis

2. space cost space of space gravelling space the space path space is space Rs. space 150 space per space sq space straight m
So comma space the space cost space of space gravelling space the space entire space path equals 425 cross times 150 equals Rs. space 63750

3. space cost space of space turfing space the space path space is space 45 space paise space per space sq space straight m
So comma space the space cost space of space turfing space the space bold semi bold short dash bold circular bold space bold grassy bold space bold plot
equals area space of space the space bold plot cross times 45 over 100
equals πr squared over 2 cross times 45 over 100
equals 22 over 7 cross times fraction numerator 31.8 squared over denominator 2 end fraction cross times 45 over 100
equals 22 over 7 cross times fraction numerator 1011.24 over denominator 2 end fraction cross times 45 over 100
equals Rs. space 715.09 end style

Answered by Rebecca Fernandes | 28th Mar, 2017, 08:57: AM