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Question

The wheels of a car are of diameter $$80\ cm$$ each. How many complete revolutions does each wheel make in $$10$$ minutes when the car is travelling at a speed of $$66$$ $$km$$ per hour


Solution

Given
Diameter of wheel $$(D) = 80$$ cm
Radius $$(r) = \dfrac {80}{2} = 40$$ cm.

$$\mbox {1 complete revolution of wheel = Circumference of wheel (C)}$$
$$C =2 \pi r = 2 \pi \times 40 = 80 \pi$$ cm
$$C = 0.8 \pi$$ m

Speed of the car $$=66$$ km / hr.$$= \dfrac {66 \times 1000}{60}$$ m/ min.

$$\therefore$$ Speed of the car $$=1100$$ m / min.

Therefore, in $$10$$min., the car will travel a distance of $$1100 \times 10 = 11000$$ m

No. of revolutions of wheel $$=\dfrac {11000}{0.8\pi} = \dfrac {11000 \times 7}{0.8 \times 22} = 4375$$

Each wheel of the car makes $$4375$$ complete revolutions in 10 min.

Mathematics

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