Question

practice: running track measures

1. the formula to find the circumference (c), the distance around a circle, is 2πr. find the distance once around the running track when r = 1/10 of a mile. use π = 3.14.

a. how i estimated:
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:
0.628.
b. how i calculated the answer:
6.28 miles.

Explanation:

Step1: Substitute values into formula

We know the formula for the circumference of a circle is $C = 2\pi r$, with $\pi=3.14$ and $r = \frac{1}{10}$ mile. Substitute these values: $C=2\times3.14\times\frac{1}{10}$.

Step2: Perform multiplication

First, $2\times3.14 = 6.28$, then $6.28\times\frac{1}{10}=0.628$ miles. This is the distance once - around the track.

Step3: Calculate distance for 10 laps

If one lap is $0.628$ miles, for 10 laps, we multiply the distance of one lap by 10. So, $0.628\times10 = 6.28$ miles.

Answer:

1.

• a. One possible estimate: We know that $\pi\approx3$. So $2\pi r\approx2\times3\times\frac{1}{10}=0.6$ miles.
• b. As calculated above, the distance once around the track is $0.628$ miles.

2.

• a. Since one - lap is about $0.6$ miles (from estimate in 1a), for 10 laps, an estimate is $0.6\times10 = 6$ miles.
• b. The runner ran $6.28$ miles.