The diameter of the driving wheel of a bus is 140 cm. How many revolutions per minute must the wheel make to maintain a speed of 66 km/h? (Use pi = 22/7 and keep units consistent.)

Introduction / Context:
This question connects circular motion with speed. Each revolution of the wheel moves the bus forward by one circumference of the wheel. So, revolutions per minute (rpm) can be found by dividing the distance travelled per minute by the wheel's circumference. The key challenge is unit conversion from km/h to m/min (or cm/min) and then consistent use of diameter and pi.

Given Data / Assumptions:

• Diameter d = 140 cm = 1.4 m
• Speed = 66 km/h
• pi = 22/7
• Circumference = pi * d
• Revolutions per minute = (distance per minute) / (circumference)

Concept / Approach:
Convert speed: 66 km/h to m/min. Compute circumference in metres. Then divide m/min by circumference to get rpm. Because pi = 22/7 is given, it yields a clean value.

Step-by-Step Solution:
Convert speed: 66 km/h = 66,000 m/h Distance per minute = 66,000/60 = 1100 m/min Circumference = pi*d = (22/7)*1.4 1.4 = 14/10, so circumference = (22/7)*(14/10) = (22*2)/10 = 44/10 = 4.4 m rpm = 1100 / 4.4 = 250 revolutions/min

Verification / Alternative check:
In 1 minute, if the wheel makes 250 revolutions, distance = 250*4.4 = 1100 m. In 1 hour, distance = 1100*60 = 66,000 m = 66 km, matching the given speed 66 km/h.

Why Other Options Are Wrong:
150 rpm: would give speed 150*4.4 = 660 m/min => 39.6 km/h. 350 rpm: would give 350*4.4 = 1540 m/min => 92.4 km/h. 550 rpm: would give far higher speed (145.2 km/h). 200 rpm: would give 200*4.4 = 880 m/min => 52.8 km/h.

Common Pitfalls:
Not converting 140 cm into metres or keeping units mixed. Forgetting to convert hours to minutes when finding distance per minute. Using radius instead of diameter in pi*d for circumference.

Final Answer:
Required speed needs 250 revolutions per minute