Answer: Paul's front wheel completed 21,147 full revolutions.
Explanation:
The distance traveled by the bike is equal to the circumference of the front wheel times the number of revolutions made by the wheel. The circumference C of a circle is given by the formula C = 2πr, where r is the radius of the circle.
In this case, the radius of the front wheel is 56 cm, so its circumference is:
C = 2πr = 2π(56 cm) ≈ 351.86 cm
To convert the distance traveled by Paul from kilometers to centimeters, we multiply by 100,000:
distance = 75.1 km = 75,100,000 cm
The number of full revolutions N made by the front wheel is therefore:
N = distance / C = 75,100,000 cm / 351.86 cm ≈ 213,470.2
However, we need to round down to the nearest integer since the wheel cannot complete a fractional revolution. Therefore:
N = 21,147
Therefore, Paul's front wheel completed 21,147 full revolutions.