Sum

The outer circumference of a circular race track is 528m. The track is everywhere 14m

wide. Calculate the cost of leveling the track at rate of 50 paise per square metre.

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#### Solution

Let inner radius = r width(d) = 14m

Outer radius = R

Outer circumference of track = 2 𝜋𝑟

∴ 2 𝜋𝑟 = 528

`2 ×22/7× R = 528 ⇒ R =528×7/2×22= 84 m`

Inner radius r = R – d = 84 – 14 = 70m

Area of track = (area of outer circle) – (area of inner circles)

= 𝜋𝑅^{2} − 𝜋𝑟^{2}

`= pi(R^2 − r^2) =22/7(84^2 − 70^2)`

`=22/7(84 + 70)(84 − 70) =22/7× 154 × 14`

= 6776 𝑚^{2}

Cost of leveling 𝑚^{2} = 𝑅𝑠. 0.50

Total cost of leveling track = 6776 ×`1/2`= 𝑅𝑠. 3388

Concept: Circumference of a Circle

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