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 .8 mil .8 mil 1.6 mi. 1.6 mi. 3.1 mi. 3.1 mi. 18.8 mi
Answers
GPT-4o mini
To find the distance to walk all the way around the circular path, we first need to determine the radius of the circle. Since the sidewalk through the middle is half a mile long, this means that the diameter of the circular path is 0.5 miles.
The radius \( r \) is half the diameter:
\[
r = \frac{0.5 \text{ miles}}{2} = 0.25 \text{ miles}
\]
Now we can use the formula for the circumference \( C \) of a circle, which is:
\[
C = 2 \pi r
\]
Substituting the radius into the formula:
\[
C = 2 \pi (0.25) = 0.5 \pi
\]
Now, we can calculate \( 0.5 \pi \):
\[
0.5 \pi \approx 0.5 \times 3.1416 \approx 1.5708 \text{ miles}
\]
Rounding to one decimal place, we find that the distance to walk all the way around the circular path is approximately:
\[
1.6 \text{ miles}
\]
So, the answer is **1.6 mi.**
The radius \( r \) is half the diameter:
\[
r = \frac{0.5 \text{ miles}}{2} = 0.25 \text{ miles}
\]
Now we can use the formula for the circumference \( C \) of a circle, which is:
\[
C = 2 \pi r
\]
Substituting the radius into the formula:
\[
C = 2 \pi (0.25) = 0.5 \pi
\]
Now, we can calculate \( 0.5 \pi \):
\[
0.5 \pi \approx 0.5 \times 3.1416 \approx 1.5708 \text{ miles}
\]
Rounding to one decimal place, we find that the distance to walk all the way around the circular path is approximately:
\[
1.6 \text{ miles}
\]
So, the answer is **1.6 mi.**