The wheel of a car covers a distance of 44 km in 5000 revolutions. The

The wheel of a car covers a distance of 44 km in 5000 revolutions. The radius of the wheel is :

14 cm
7 cm
28 cm
25 cm
This question was previously asked in
UPSC CISF-AC-EXE – 2023
The correct answer is A.
The distance covered by a wheel in one revolution is equal to its circumference (C = 2πr). The total distance covered is the number of revolutions multiplied by the circumference.
Total distance = 44 km = 44,000 meters.
Number of revolutions = 5000.
Circumference C = Total distance / Number of revolutions = 44,000 m / 5000 = 44/5 m = 8.8 m.
Using the formula for circumference C = 2πr:
8.8 m = 2 * (22/7) * r
8.8 = (44/7) * r
r = (8.8 * 7) / 44 = (88/10 * 7) / 44 = (2 * 44 / 10 * 7) / 44 = (2/10) * 7 = 0.2 * 7 = 1.4 meters.
Converting meters to centimeters: 1.4 meters * 100 cm/meter = 140 cm.
However, 140 cm is not among the options. Let’s re-check the calculation assuming the distance was 4.4 km instead of 44 km, as the options are relatively small values in cm.
If distance = 4.4 km = 4400 m.
Circumference C = 4400 m / 5000 = 44/50 m = 22/25 m = 0.88 m.
Using C = 2πr:
0.88 m = 2 * (22/7) * r
0.88 = (44/7) * r
r = (0.88 * 7) / 44 = (88/100 * 7) / 44 = (2 * 7) / 100 = 14/100 = 0.14 meters.
Converting meters to centimeters: 0.14 meters * 100 cm/meter = 14 cm.
This matches option A. Given the options, it is highly probable that the intended distance in the question was 4.4 km, not 44 km.
Assuming a typo in the question is necessary to match the provided options. In competitive exams, if the exact calculation doesn’t yield any option, one might consider potential typos or approximations. In this case, a factor of 10 difference in distance leads to a factor of 10 difference in radius, making 14 cm the most likely intended answer corresponding to a distance of 4.4 km.