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To determine how many revolutions the bicycle wheel will make, we can use the following steps:

1. **Calculate the circumference of the wheel**:  
   The circumference \( C \) of a circle is given by \( C = \pi \times \text{diameter} \).  
   For a wheel with a diameter of 25 inches, the circumference is:
   \[
   C = \pi \times 25 \approx 78.54 \text{ inches}
   \]

2. **Convert the distance traveled from miles to inches**:  
   Since there are 63,360 inches in a mile, the distance traveled (3 miles) in inches is:
   \[
   3 \times 63,360 = 190,080 \text{ inches}
   \]

3. **Calculate the number of revolutions**:  
   The number of revolutions is the total distance divided by the circumference of the wheel:
   \[
   \text{Revolutions} = \frac{190,080}{78.54} \approx 2420.57
   \]

So, the bicycle wheel will make approximately **2,420.57 revolutions** to travel a distance of 3 miles.

Would you like further details or have any questions about this?

Here are some related questions to deepen understanding:
1. How would the number of revolutions change if the wheel diameter were larger or smaller?
2. What would the answer be if the distance traveled was given in kilometers instead of miles?
3. How does the wheel's circumference affect the distance covered per revolution?
4. If a cyclist maintained a speed that resulted in 100 revolutions per minute, how long would it take to travel 3 miles?
5. How many revolutions would a 20-inch diameter wheel make over the same distance?

**Tip:** Knowing unit conversions, such as inches to miles or feet to inches, can be very helpful in solving real-world measurement problems like this one.

How many revolutions will a bicycle wheel of diameter 25 inches make as the bicycle travels a distance of 3 miles?

Learn how to calculate the number of revolutions a 25-inch diameter bicycle wheel makes over a 3-mile distance. This solution involves converting miles to inches, calculating circumference, and using key geometry concepts. Ideal for high school students in Grades 9-10.

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