To solve for the radius of the bicycle tire, we need to understand the relationship between the distance traveled, the number of rotations, and the radius of the tire.

The formula for the distance traveled in one full rotation of a tire is the circumference of the tire, which can be expressed as:

$C = 2 \pi r$

where:

• $C$ is the circumference,
• $r$ is the radius of the tire.

If the tire completes 10 rotations, the total distance traveled is 10 times the circumference:

$\text{Total Distance} = 10 \times C = 10 \times 2 \pi r$

We are told that the total distance traveled is 879.2 inches, so we set up the equation:

$10 \times 2 \pi r = 879.2$

Now, solve for $r$:

$20 \pi r = 879.2$

$r = \frac{879.2}{20 \pi}$

$r \approx \frac{879.2}{62.832}$

$r \approx 14$

So, the radius of the tire is approximately 14 inches.

Would you like more details on the solution? Or have other questions about this problem?

Here are some follow-up questions:

1. How would the equation change if the tire traveled a different distance, say 1000 inches?
2. How does the value of $\pi$ affect the calculation of the radius?
3. If the tire had a radius of 10 inches, how far would it travel after 15 rotations?
4. Can we use the same formula for non-circular objects to find their radius?
5. What is the relationship between the diameter of the tire and the radius in this context?

Tip: When dealing with problems involving rotations and circular motion, always remember that the total distance traveled is directly related to the circumference, which depends on the radius.