Question

practice: running track measures

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:
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:

1. 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 \( C = 2\pi r \):
\( C=2\times3.14\times\frac{1}{10} \)

Step3: Perform the multiplication

First, calculate \( 2\times3.14 = 6.28 \), then \( 6.28\times\frac{1}{10}=0.628 \)

Step1: Identify the distance per lap

From part 1, we know that one lap (the circumference) is \( 0.628 \) miles.

Step2: Calculate the distance for 10 laps

To find the distance for 10 laps, we multiply the distance per lap by 10: \( 0.628\times10 \)

Step3: Perform the multiplication

\( 0.628\times10 = 6.28 \)

Answer:

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

2. b. How I calculated the answer: