Question

A map of a public park shows a circular pond. There is a bridge along a diameter of the pond that is 0.25 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?

Answer 1

Your friend walks approximately 0.3925 miles farther than you along the curved path of the pond.

Step-by-step explanation:

To find out how much farther your friend walks, we need to compare the distance along the bridge to the distance halfway around the pond. The bridge is a straight line across the pond, which is the same as the diameter of the pond. The diameter is 0.25 miles long. Your friend walks halfway around the pond, which is equivalent to walking half the circumference of the pond. The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. Since the bridge is the diameter, it is equal to 2 times the radius, or 2r. So the distance your friend walks is half the circumference or (1/2)(2πr) = πr. Since the diameter is 0.25 miles, the radius is half of that, or 0.125 miles. Plugging this into the formula, we find that your friend walks π(0.125) miles. To find a numerical approximation, we can use the fact that π is approximately 3.14, so your friend walks 3.14(0.125) miles. This simplifies to approximately 0.3925 miles. Therefore, your friend walks approximately 0.3925 miles farther than you along the curved path of the pond.

Answer 2

The circumference of a circle is pi times diameter, so half-way around the pond is (1/2)pi times diameter.


`(\pi)/(2) = 1.57`

The difference between walking around the pond and walking across the bridge is: 1.57d - d = 0.57d

Plug in diameter of 0.25

0.25*0.57 = 0.14 miles