Question

practice: running track measures

circle with radius \\( \frac{1}{10} \\) mile

1. the formula to find the circumference (c), the distance around a circle, is \\( 2\pi r \\). find the distance once around the running track when \\( r = \frac{1}{10} \\) of a mile. use \\( \pi = 3.14 \\).

a. how i estimated:
handwritten: 0.628
b. how i calculated the answer:

1. if a runner did 10 laps around the track, how far did she run?

a. how i estimated:
b. how i calculated the answer:

Explanation:

Problem 1

Part b: How I calculated the answer:

Step1: Identify the formula and values

The formula for the circumference of a circle is \( C = 2\pi r \). We know that \( r=\frac{1}{10} \) mile and \( \pi = 3.14 \).

Step2: Substitute the values into the formula

Substitute \( r=\frac{1}{10} \) and \( \pi = 3.14 \) into \( C = 2\pi r \). So we have \( C=2\times3.14\times\frac{1}{10} \).

Step3: Perform the multiplication

First, calculate \( 2\times3.14 = 6.28 \). Then, multiply by \( \frac{1}{10} \): \( 6.28\times\frac{1}{10}=0.628 \) miles.

Step1: Recall the circumference from Problem 1

From Problem 1, we found that the circumference \( C = 0.628 \) miles (this is the distance for one lap).

Step2: Calculate the distance for 10 laps

To find the distance for 10 laps, we multiply the circumference (distance per lap) by the number of laps (10). So the distance \( D=10\times C \).

Step3: Substitute the value of \( C \)

Substitute \( C = 0.628 \) into the formula: \( D = 10\times0.628=6.28 \) miles.

Answer:

The distance once around the running track is \( 0.628 \) miles.

Problem 2

Part b: How I calculated the answer: