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Question

How long will a man take to make a round of a circular field of radius $$21\,m,$$ cycling at the speed of $$8 \,km/h$$ ?

Solution
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From the question,
Radius of the circular field, $$r = 21 \,m$$
Cycling at the speed of $$= 8 \,km/h$$
$$= \dfrac{8 \times 1000} {3600} \,m/s$$....[Because $$1 \,km = 1000 \,m , 1 \,hr = 3600 \,sec$$]
$$= \dfrac{8000} {3600}$$
$$= \dfrac{80} {36}...$$ [divide by $$4$$]
$$= \dfrac{20} {9} \,m/s$$
Distance covered by the cyclist = Circumference of the circular field
$$= 2 \pi r$$
$$= 2 \times \dfrac{22}{7} \times 21$$
$$= 2 \times 22 \times 3$$
$$= 132 \,m$$
Time taken by the cyclist to cover the field = (Distance covered by the cyclist / Speed of the cyclist)
$$= \dfrac{132} {\dfrac{20}{9}}$$
$$= 132 \times \dfrac{9}{20}$$
$$= 33 \times \dfrac{9} {5}$$
$$= 59.4 \,sec$$

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