The circumference of a circular playground is 528 m. The total expenditure of repairs of the ground at the rate of Rs.1.50 per square meter will be Rs. ____.

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Accepted Answer

The expenditure to repair the ground will be Rs. 33264.
Concept- Given in the question statement is the circumference of a circle. We have to know the formula to calculate the circumference of a circle which is,
Circumference =

Where, R = Radius of the circle.
Using the above-mentioned formula of the circumference of a circle as an equation, we will find out the value of R and then, use it in the formula of “Area of a circle”, which goes as follows:

Finally, we will have to multiply the calculated area of the playground with the cost of repair per unit, to obtain the total expenditure of repairs. Given, circumference of a circular playground is 528 m.
Let's assume that "R" is the circle's radius.

528 = (2 × π × R)

R = 528 (2 × π)

⇒ R = 528 2 × 227 π = 227

⇒ R = 528 × 7 2 × 22

⇒ R = 84 m

Therefore,

= 227 × 842 π = 227

= 227 × 84 × 84

Since, the cost of repairs per unit sq. m. is Rs.1.50, total cost of repairing the full playground

Hence, the correct answer is Rs.33264.

528=(2×π×R)

R=
    
     528
    
     (2×π)

⇒R=
    
     528

2×
        
         22
        7

π=
      
       22
      7

⇒R=
    
     528×7
    
     2×22

⇒R=84m
  Therefore,

=

22
      7
     
     ×
      
       84
      2

π=
      
       22
      7

=

22
      7
     
     ×84×84
   
                                     Since, the cost of repairs per unit sq. m. is Rs.1.50, total cost of repairing the full playground Hence, the correct answer is Rs.33264.

The circumference of a circular playground is 528 m. The total expenditure of repairs of the ground at the rate of Rs.1.50 per square meter will be Rs. ____.

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