Question

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 18.8 mi 18.8 mi 1.6 mi. 1.6 mi. .8 mil .8 mil 3.1 mi.

Answer 1

To find the distance around the circular path, we can use the relationship between the radius of the circular path and the circumference.

1. **Understanding the sidewalk**: The sidewalk through the middle is given as half a mile (0.5 miles) and represents the diameter of the circular path.

2. **Radius of the circular path**: The radius (r) is half the diameter. Therefore,
\[
r = \frac{0.5 \text{ miles}}{2} = 0.25 \text{ miles}
\]

3. **Calculating the circumference**: The formula for the circumference (C) of a circle is given by:
\[
C = 2 \pi r
\]
Substituting the radius we found:
\[
C = 2 \pi (0.25) \approx 2 \times 3.14 \times 0.25 = 1.57 \text{ miles}
\]

4. **Rounding to one decimal place**: The circumference is approximately 1.57 miles, which rounded to one decimal place is:
\[
1.6 \text{ miles}
\]

Thus, the distance to walk all the way around the circular path is **1.6 miles**.

So the correct response is **1.6 mi**.