Question

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

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

1. how many times would she run around the track to do a total of 10 miles?

a. how i estimated:
b. how i calculated the answer: 159.23 laps

Explanation:

Step1: Recall the circumference formula

The formula for the circumference of a circle is $C = 2\pi r$, where $r$ is the radius of the circle. Given $r=\frac{1}{10}$ mile and $\pi = 3.14$.

Step2: Substitute values into formula

$C=2\times3.14\times\frac{1}{10}$. First, $2\times3.14 = 6.28$, then $6.28\times\frac{1}{10}=0.628$ miles.

Step3: Calculate number of laps for 10 miles

To find the number of times to run around the track for 10 miles, we use the formula $n=\frac{10}{C}$, where $n$ is the number of laps. Substitute $C = 0.628$ into the formula: $n=\frac{10}{0.628}\approx15.923$. Rounding up, we get 16 laps.

Answer:

1.
a. The estimated value of the circumference is $0.628$ miles. I estimated by substituting $r = \frac{1}{10}$ mile and $\pi=3.14$ into the formula $C = 2\pi r$.
b. First, I found the circumference $C = 2\times3.14\times\frac{1}{10}=0.628$ miles. Then, to find the number of laps for 10 miles, I divided 10 by the circumference: $\frac{10}{0.628}\approx15.923$. Rounding up, the number of laps is 16.