A wheel makes 1000 revolutions while covering a distance of 88 km.\nFind the radius of the wheel.\n(Assume no slipping and use pi = 22/7 if needed.)

Introduction:
This question tests the connection between revolutions and distance traveled by a wheel. In one revolution, a wheel covers a distance equal to its circumference. Therefore, total distance = (number of revolutions) * (circumference). When total distance and revolutions are given, we can find circumference per revolution, and then compute radius using circumference formula C = 2*pi*r. Unit conversion is important because the distance is given in km and radius will come out in metres if we convert properly.

Given Data / Assumptions:

• Number of revolutions = 1000
• Total distance = 88 km = 88000 m
• Distance per revolution (circumference) = total distance / revolutions
• Circumference formula: C = 2*pi*r
• Use pi = 22/7 for exact result

Concept / Approach:
First compute circumference of the wheel by dividing total distance by revolutions. Then solve r = C / (2*pi). Because aptitude problems often use pi = 22/7, we will compute with that to get a clean answer.

Step-by-Step Solution:
Total distance = 88 km = 88000 mCircumference C = 88000 / 1000 = 88 mC = 2*pi*r => r = C / (2*pi) = 88 / (2*pi) = 44 / piUsing pi = 22/7: r = 44 * (7/22) = 2 * 7 = 14 m

Verification / Alternative Check:
If radius is 14 m, circumference = 2*pi*14 = 28pi. With pi = 22/7, circumference = 28 * 22/7 = 88 m. Over 1000 revolutions, distance = 1000*88 = 88000 m = 88 km, exactly matching the given distance. So the radius is confirmed.

Why Other Options Are Wrong:
13, 12, 11, 10 m: would produce circumferences smaller than 88 m, meaning 1000 revolutions would cover less than 88 km.

Common Pitfalls:
Forgetting to convert 88 km into metres before dividing.Using C = pi*r or C = pi*d incorrectly.Dividing by pi instead of 2*pi when finding radius.Rounding pi and missing the exact integer radius.

Final Answer:
14 m