A boy is cycling in such a way that the wheels of his bicycle are making 140 revolutions per minute. If the diameter of a wheel is 60 cm, calculate the speed (in km / hr) at which the boy is cycling.

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Solution

Diameter of the wheel = 60 cm

Therefore, Radius of the wheels = 30 cm

Circumference of the wheels $= 2 π r = 2 \times \frac{22}{7} \times 30 = \frac{1320}{7}$ cm

Distance covered by the wheel in 1 revolution = $\frac{1320}{7}$ cm

Therefore, Distance covered by the wheel in 140 revolutions $= (\frac{1320}{7} \times 140 \times \frac{1}{100})$ m

$= (\frac{1320 \times 140}{7 \times 100} \times \frac{1}{1000}) k m = \frac{264}{1000} k m$

Now,

Distance covered by the wheel in 1 minute = Distance covered by the wheel in 140 revolution = $\frac{264}{1000} k m$

Therefore, Distance covered by the wheel in 1 hour = $\frac{264}{1000} \times 60 = 15.84 k m / h$

Hence, the speed at which the boy is cycling is $15.84 k m / h$

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