Final answer:
Shen's bicycle wheel, with a diameter of 0.3 meters, turns approximately 31.8 times over a distance of 30 meters.
Step-by-step explanation:
To calculate how many times the wheel turns as the bicycle travels 30 meters, we need to use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius of the circle.
It's important to note that the diameter of the wheel is given as 0.3 meters, so the radius of the wheel is half that, which is 0.15 meters.
The circumference of Shen's bicycle wheel is then C = 2π(0.15) meters. To find out how many times the wheel turns over a distance of 30 meters, we divide the total distance by the circumference:
Number of revolutions = Total distance traveled / Circumference of wheel
Number of revolutions = 30 m / (2π(0.15)) m
Number of revolutions = 30 / (2π(0.15))
Number of revolutions = 30 / (0.3π)
Number of revolutions = 100/π revolutions
Therefore, Shen's bicycle wheel turns approximately 100/π or about 31.8 times when traveling a distance of 30 meters.