To solve the problem step by step, we will follow these steps:
### Step 1: Convert the speed from km/hr to m/min
The speed of the cyclist is given as 16.5 km/hr. To convert this to meters per minute, we use the following conversion factors:
1 km = 1000 meters
1 hour = 60 minutes
\[
\text{Speed in m/min} = 16.5 \, \text{km/hr} \times \frac{1000 \, \text{m}}{1 \, \text{km}} \times \frac{1 \, \text{hr}}{60 \, \text{min}}
\]
Calculating this gives:
\[
\text{Speed in m/min} = 16.5 \times \frac{1000}{60} = 275 \, \text{m/min}
\]
### Step 2: Calculate the total distance traveled in 45 minutes
Now that we have the speed in meters per minute, we can calculate the total distance traveled in 45 minutes:
\[
\text{Distance} = \text{Speed} \times \text{Time}
\]
\[
\text{Distance} = 275 \, \text{m/min} \times 45 \, \text{min} = 12375 \, \text{meters}
\]
### Step 3: Calculate the circumference of the wheel
The diameter of the wheel is given as 21 cm. To find the circumference (the distance traveled in one complete revolution of the wheel), we use the formula:
\[
\text{Circumference} = \pi \times \text{Diameter}
\]
Using \(\pi \approx \frac{22}{7}\):
\[
\text{Circumference} = \frac{22}{7} \times 21 \, \text{cm}
\]
Calculating this gives:
\[
\text{Circumference} = 66 \, \text{cm}
\]
### Step 4: Convert the circumference to meters
Since the distance traveled is in meters, we need to convert the circumference from centimeters to meters:
\[
\text{Circumference in meters} = \frac{66 \, \text{cm}}{100} = 0.66 \, \text{meters}
\]
### Step 5: Calculate the number of revolutions
Now, we can find the number of revolutions made by the wheel during the journey by dividing the total distance by the circumference of the wheel:
\[
\text{Number of revolutions} = \frac{\text{Total distance}}{\text{Circumference}}
\]
\[
\text{Number of revolutions} = \frac{12375 \, \text{meters}}{0.66 \, \text{meters}} \approx 18750
\]
### Final Answer
The wheel will make approximately **18750 revolutions** during the journey.
---
