A map of a public park shows a circular pond. There is a bridge along a diameter of the pond that is 0.55 mi long. You walk across the bridge, while your friend walks halfway around the pond to meet you at the other side of the bridge. How much farther does your friend walk? Round your answer to the nearest hundredth. Use 3.14 for π.
Your friend walks about (answer) miles farther than you
bridge: 0.55
1/2 circumference: 1/2 π * 0.55
so, the difference is 0.55(π/2 - 1) = ____
To calculate how much farther your friend walks than you, we need to find the circumference of the circle.
We know that the bridge is along the diameter of the pond, which means it divides the circle into two equal parts. Since the length of the bridge is 0.55 mi, the radius of the circle would be half of that, which is 0.275 mi.
Now, we can use the formula to find the circumference of a circle:
Circumference = 2 * π * radius
Substituting the values, we get:
Circumference = 2 * 3.14 * 0.275
= 1.73 mi (rounded to two decimal places)
This is the total distance your friend walks around the pond. However, you only walk across the bridge, which is the diameter of the circle. So, your distance is:
Distance = 0.55 mi
To find how much farther your friend walks, subtract your distance from the total circumference:
Difference = Circumference - Distance
= 1.73 mi - 0.55 mi
≈ 1.18 mi (rounded to two decimal places)
Therefore, your friend walks about 1.18 miles farther than you.