A race track is in the shape of a ring whose inner and outer circumferences are 440 m and 506 m,respectively. What is the cost of levelling the track at ₹6/m$$^2$$? (Take $$\pi = \frac{22}{7}$$ )

Outer circumference = 506 m

2$$\pi$$ r = 506

r = 253/$$\pi$$

Inner circumference = 440 m

2$$\pi$$ r = 440

r =  220/$$\pi$$

Area = $$\pi r^2$$

Area of the track = outer area - inner area

= $$\pi \times (253/\pi)^2 - \pi \times (220/\pi)^2$$

=$$\frac{1}{\pi}(253^2 - 220^2)$$

=$$\frac{1}{\pi}(64009 - 48400)$$

=$$\frac{1}{22/7} \times(15609) = 4966.5 m^2$$

The cost of leveling the track = Rs.6/m$$^2$

Total cost = 4966.5 $$\times$$ 6 = Rs.29799