Question : A horse takes $2\frac{1}{2}$ seconds to complete a round around a circular field. If the speed of the horse was 66 m/sec, then the radius of the field is: [Given $\pi =\frac{22}{7}$]
Option 1: 25.62 m
Option 2: 26.52 m
Option 3: 25.26 m
Option 4: 26.25 m
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Correct Answer: 26.25 m
Solution :
Distance covered in one revolution = Circumference of circular field = $2\pi r$
Speed of horse = 66 m/sec
Time = $2\frac{1}{2}$ = $\frac{5}{2}$ sec
Distance covered = 66 × $\frac{5}{2}$ = 165 m
Distance covered = circumference of the circle = $2\pi r$
⇒ $165 = 2\pi r$
⇒ $165 = 2×\frac{22}{7}×r$
⇒ $r = \frac{165×7}{2×22}$
= 26.25
Hence, the correct answer is 26.25 m.
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