The bicycle tire has a radius of 13 inches. What distance will the tire have traveled in a straight line after 1 revolution? Round to the nearest tenth of an inch.

Understand the Problem

The question is asking for the distance a bicycle tire will travel in a straight line after one complete revolution. To solve this, we will use the formula for the circumference of a circle, which is C = 2πr, where r is the radius of the tire.

Answer

$81.6$ inches

Steps to Solve

Identify the formula for circumference

To find the distance the tire travels in one revolution, we use the circumference formula, which is given by $C = 2\pi r$, where $r$ is the radius of the tire.

Substitute the radius into the formula

Given that the radius $r$ of the tire is 13 inches, we substitute this value into the formula:

$$ C = 2\pi \times 13 $$

Calculate the circumference

Now, we calculate the value using $\pi \approx 3.14$:

$$ C \approx 2 \times 3.14 \times 13 $$

Perform the multiplication

Calculating the above expression step by step:

First, calculate $2 \times 13 = 26$.
Then, multiply this by $\pi$:

$$ C \approx 26 \times 3.14 \approx 81.64 $$

Round to the nearest tenth

Finally, we round the result to the nearest tenth:

$$ C \approx 81.6 \text{ inches} $$

The distance the tire will have traveled in a straight line after one revolution is approximately $81.6$ inches.

More Information

The calculation for the circumference of a circle is crucial not only in this context but also in various practical applications such as engineering, design, and even in determining distances in sports.

Tips

Confusing diameter and radius: Remember that the radius is half the diameter, and use the radius in the formula.
Incorrectly calculating the value of $\pi$: Ensure to use a reliable approximation, such as $3.14$ or use a calculator for more precision.

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