Wyatt wants to walk at the park, but doesn't know how long the path is. He knows it is a circular path with a sidewalk through the middle. The sidewalk through the middle is half a mile long. How far is it to walk all the way around the circular path? Round your answer to one decimal place. (1 point)

Responses

1.6 mi.
1.6 mi.

18.8 mi
18.8 mi

3.1 mi.
3.1 mi.

.8 mil

1 answer

To find out how far it is to walk all the way around the circular path, we first need to determine the radius of the circular path.

Since the sidewalk through the middle is half a mile long, and this is likely meant to represent the diameter of the circular path, the radius \( r \) of the circular path would be half of the diameter:

\[ r = \frac{\text{diameter}}{2} = \frac{0.5 \text{ mi}}{2} = 0.25 \text{ mi} \]

Now, we can find the circumference \( C \) of the circular path using the formula for the circumference of a circle:

\[ C = 2 \pi r \]

Substituting the radius we just found:

\[ C = 2 \pi (0.25) \]

Calculating this:

\[ C = 0.5\pi \]

Using the approximation \( \pi \approx 3.14 \):

\[ C \approx 0.5 \times 3.14 \approx 1.57 \text{ mi} \]

Rounding this to one decimal place gives us:

\[ C \approx 1.6 \text{ mi} \]

So, the correct response is:

1.6 mi.