A wheel of diameter 40 cm travels a distance of 176 m.\nHow many revolutions does the wheel make while covering this distance?\n(Assume no slipping.)

Introduction:
This question tests the relationship between circular motion and linear distance. Each full revolution of a wheel covers a distance equal to the wheel’s circumference. Therefore, the number of revolutions equals total distance traveled divided by the circumference. The main challenge is unit consistency: diameter is given in cm while distance is given in m, so we must convert to the same unit before dividing. This is a standard aptitude question that checks circumference formula usage and careful unit conversion.

Given Data / Assumptions:

• Wheel diameter = 40 cm
• Distance traveled = 176 m
• Convert 176 m to cm: 176 m = 17600 cm
• Circumference C = pi * d
• Number of revolutions = distance / circumference

Concept / Approach:
Compute circumference using C = pi*d. Convert distance to cm to match. Then revolutions = 17600 / (40*pi). Use pi = 22/7 to get an exact integer result, which is typical in aptitude problems.

Step-by-Step Solution:
Distance = 176 m = 17600 cmCircumference = pi * d = pi * 40 = 40pi cmRevolutions = 17600 / (40pi) = 440 / piUsing pi = 22/7: revolutions = 440 * (7/22) = 20 * 7 = 140

Verification / Alternative Check:
If revolutions are 140, then distance covered = 140 * circumference = 140 * 40pi cm = 5600pi cm. Using pi = 22/7, distance = 5600 * 22/7 = 800 * 22 = 17600 cm = 176 m. This matches the given distance exactly, confirming correctness.

Why Other Options Are Wrong:
240 or 340: too high, would require either a much smaller wheel or longer distance.40 or 120: too low, typically from forgetting unit conversion or using radius instead of diameter in circumference.

Common Pitfalls:
Not converting metres to centimetres.Using circumference as 2*pi*d instead of pi*d.Using radius 40 cm instead of diameter 40 cm.Rounding pi too early and losing exactness.

Final Answer:
140