To solve this problem, we need to calculate the distance traveled by the wheel for the given number of rotations. The distance traveled in one rotation is equal to the circumference of the wheel. The formula for the circumference is:

$\text{Circumference} = 2 \pi r$

where $r$ is the radius. Let's calculate the distances for each case:

Given:

• Radius ($r$) = 35 cm
• Number of rotations = 1, 5, and 30

Step 1: Calculate the Circumference

$\text{Circumference} = 2 \pi (35) = 70 \pi \, \text{cm}$

Step 2: Calculate Distances

1. For 1 rotation ($x$): $x = 70 \pi \approx 70 \times 3.1416 = 219.91 \, \text{cm}$

2. For 5 rotations ($y$): $y = 5 \times 70 \pi = 350 \pi \approx 350 \times 3.1416 = 1099.56 \, \text{cm}$

3. For 30 rotations ($z$): $z = 30 \times 70 \pi = 2100 \pi \approx 2100 \times 3.1416 = 6597.34 \, \text{cm}$

Final Table:

Let me know if you'd like to discuss this further!

Questions for Better Understanding:

1. Why do we use $2 \pi r$ to calculate the circumference?
2. How can we verify these results using real-world measurements?
3. What happens if the radius of the wheel is doubled?
4. How does the number of rotations affect the total distance?
5. Can you think of a practical example where this calculation might be applied?

Tip:

Always ensure your units are consistent throughout your calculations to avoid confusion or errors.