Question : The diameter of a circular wheel is 7 m. How many revolutions will it make in travelling 22 km?
Option 1: 100
Option 2: 400
Option 3: 500
Option 4: 1000
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Correct Answer: 1000
Solution : The distance covered in one revolution of a wheel is equal to its circumference, $C$. $C = \pi d$, where $d$ is the diameter of the wheel. We have the diameter of the wheel is 7 m. $\therefore C = \pi \times 7 = \frac{22}{7}×7 = 22\;\mathrm{m}$ In one revolution, the wheel covers approximately 22 m. The wheel travels 22 km, which is equal to 22000 m. $\therefore$ Number of revolutions $=\frac{22000}{22} = 1000$ Hence, the correct answer is 1000.
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Question : The diameter of a wheel on a bicycle is 21 cm. The cyclist takes 45 minutes to reach a destination at a speed of 16.5 km/hr. How many revolutions will the wheel make during the journey?
Option 1: 12325
Option 2: 18750
Option 3: 21000
Option 4: 24350
Question : The diameter of each wheel of a car is 70 cm. If each wheel rotates 400 times per minute, then the speed of the car (in km/hr) is: (Take $\pi=\frac{22}{7}$)
Option 1: 0.528
Option 2: 528
Option 3: 52.8
Option 4: 5.28
Question : Two trains start from a certain place on two parallel tracks and in the same direction. The speeds of the trains are 45 km/hr and 40 km/hr respectively. The distance between the two trains after 45 minutes will be:
Option 1: 2 km 500 m
Option 2: 2 km 750 m
Option 3: 3 km 750 m
Option 4: 3 km 250 m
Question : An athlete runs 8 times around a circular field of radius 7 m in 3 minutes 40 seconds. His speed (in km/hr) is: (Take $\pi=\frac{22}{7}$ )
Option 1: $\frac{72}{25}$
Option 2: $\frac{118}{25}$
Option 3: $\frac{144}{25}$
Option 4: $\frac{108}{25}$
Question : How many metres of 2-m-wide cloth will be required to make a conical tent with a diameter of the base of 14 m and a slant height of 9 m ignoring wastage?
Option 1: 66 m
Option 2: 88 m
Option 3: 99 m
Option 4: 77 m
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