Question

The outer circumference of a circular race-track is 525 m. The track is everywhere 14 m wide. Calculate the cost of leveling the track at the rate of 50 paise per square meter (use π = \(\frac{22}7\)}

Answer 1

Given, 

Circumference of outer circle = 525 m 

Let radius of outer circle = R₂ m 

Let radius of inner circle = R₁ m 

So, 

R₂ - R₁ = 14 (equation 1) 

= 2πR₂ = 525

R₂ = \(\frac{525}2\times\frac{7}{22}\) = 83.52 m

Put value of R₁ in equation first 

= 83.52 – R₁ = 14 

= - R₁ = 14 – 83.52 

= R₁ = 69.52 m 

Area of path = \(πR_2^2 - πR_1^2\)

Cost of leveling the path = 6733.76×.50 = Rs 3388