A wheel travelled 55 km in 10001000 rotations. Find the diameter of the wheel to the nearest cm

1. Break Down the Problem

To find the diameter of the wheel, we need to:

1. Calculate the circumference of the wheel based on the total distance traveled.
2. Use the circumference to find the diameter.

2. Relevant Concepts

The relationship between the circumference $C$ and the diameter $d$ of a circle is given by the formula: $C = \pi d$ Also, the circumference can be determined by dividing the total distance traveled by the number of rotations: $C = \frac{\text{Total Distance}}{\text{Number of Rotations}}$

3. Analysis and Detail

1. Calculate the Circumference:

   • Total Distance traveled by the wheel = 55 km = $55 \times 1000$ m = 55000 m
   • Number of Rotations = 1000

   $C = \frac{55000 \, \text{m}}{1000} = 55 \, \text{m}$

2. Find the Diameter: Using the circumference to find the diameter: $d = \frac{C}{\pi} = \frac{55}{\pi}$

   Using $\pi \approx 3.14$: $d \approx \frac{55}{3.14} \approx 17.5 \, \text{m}$

   To convert this measurement to centimeters: $d \approx 17.5 \, \text{m} \times 100 = 1750 \, \text{cm}$

4. Verify and Summarize

• The circumference calculated is consistent with the total distance and the number of rotations.
• The diameter calculated is $1750$ cm when rounded to the nearest cm.

Final Answer

The diameter of the wheel is approximately 1750 cm.