To find out how much distance the wheel will cover when it rotates 450 times, we need to calculate the circumference of the wheel and then multiply that by the number of rotations.

Step 1: Calculate the Circumference of the Wheel

The formula for the circumference $C$ of a circle is:

$C = 2\pi r$

Where:

• $r$ is the radius of the wheel,
• $\pi$ is approximately $3.14$.

Given:

• $r = 21 \, \text{cm}$,
• $\pi = 3.14$.

Now, calculate the circumference:

$C = 2 \times 3.14 \times 21 = 131.88 \, \text{cm}$

Step 2: Convert Circumference to Meters

Since 1 meter = 100 cm, we convert the circumference into meters:

$C = \frac{131.88}{100} = 1.3188 \, \text{m}$

Step 3: Calculate the Total Distance Covered

If the wheel rotates 450 times, the total distance covered will be:

$\text{Total Distance} = \text{Circumference} \times \text{Number of Rotations}$

$\text{Total Distance} = 1.3188 \, \text{m} \times 450 = 593.46 \, \text{m}$

Thus, the wheel will cover a distance of 593.46 meters after 450 rotations.

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Would you like further details or clarifications on any step? Here are some additional questions you might find interesting:

1. How would the distance change if the radius of the wheel were doubled?
2. How do you calculate the distance for multiple wheels with different radii?
3. What would happen if the wheel rotated 1000 times instead of 450?
4. How do you convert from centimeters to meters in general?
5. What if we used a more precise value of $\pi$, like 3.14159?

Tip: Always remember to convert your units to match the desired final answer (e.g., cm to meters).