Determining the Time to Circumnavigate a Circular Park: Understanding the Steps and Calculations

When planning a visit to a circular park, it's important to understand the time required to walk around it. This guide breaks down the process of calculating the time taken to cover the entire circumference of a circular park given its diameter and walking speed. Whether you are an enthusiast planning a stroll, or someone conducting a practical exercise, this will provide you with the necessary steps.

Calculations and Formulae

The circumference of a circle is calculated using the formula π × diameter. Understanding this key concept is crucial for solving problems involving circular paths and distances.

Step 1: Calculate the Circumference

Given a park with a diameter of 420 meters, the circumference can be calculated as follows:

[text{Circumference} pi times text{Diameter}]

Substituting the given diameter:

[text{Circumference} pi times 420 , text{meters} 1319.08 , text{meters}]

Step 2: Convert Speed from Kilometers per Hour to Meters per Hour

The walking speed is given as 4.4 kilometers per hour (km/hr). To convert this into meters per hour (m/hr), simply multiply by 1000:

[text{Speed in m/hr} 4.4 , text{km/hr} times 1000 4400 , text{meters per hour}]

Step 3: Calculate the Time Required to Walk the Circumference

To find the time required to cover the circumference, divide the total distance by the speed:

[text{Time} frac{text{Distance}}{text{Speed}} frac{1319.08 , text{meters}}{4400 , text{meters per hour}}]

This gives:

[text{Time} 0.30 , text{hours}]

Step 4: Convert Hours to Minutes

To convert the time from hours to minutes, multiply by 60:

[text{Time in minutes} 0.30 , text{hours} times 60 , text{minutes per hour} 90 , text{minutes}]

Alternative Calculations and Corrections

Occasionally, there may be discrepancies or alternative methods. For instance, one might argue that the diameter is 420 meters, but the circumference might be simplified as (3.14 times 420 1319.08) meters which is approximately 1.32 kilometers. In such cases, the calculation would be:

[text{Time} frac{1.32 , text{kilometers}}{4.4 , text{kilometers per hour}} 0.58 , text{hours} 1 , text{minute}]

This suggests a much shorter time, but remember, the key is to ensure all units are consistent (meters for both distance and speed).

Additional Calculations

To further explore the relationship between the diameter and the radius, remember that the radius is half the diameter:

[text{Radius} frac{text{Diameter}}{2} frac{420 , text{meters}}{2} 210 , text{meters}]

The circumference can also be calculated using the formula (C 2pi r), which in this case would be:

[text{Circumference} 2 times 3.14 times 210 , text{meters} 1319.08 , text{meters}]

Conclusion

By following these steps, one can accurately determine the time required to walk around a circular park given its diameter and the speed at which one is walking. The key is to ensure units are consistent and all calculations are performed methodically. Whether for planning a visit, a study exercise, or to understand the relationship between distance and speed, this method provides a comprehensive solution.