To solve this problem, you will need to know the formula to find the circumference of a circle given the diameter of a circle. After calculating the circumference, you will then divide this result by 5 to obtain the final answer needed for this problem.
The circumference of a circle is found using the formula C = 2πr.
[tex]C = 2\pi r[/tex]
We are given the diameter. The radius can be found using r = D/2.
[tex]\displaystyle r=\frac{D}{2}[/tex]
[tex]\displaystyle r=\frac{14}{2}[/tex]
[tex]r=7[/tex]
Plug in the radius to the formula for a circle's circumference: C = 2πr.
[tex]C = 2 \pi (7)[/tex]
Rearrange the equation to distribute the 7 into the 2π.
[tex]C = 7(2\pi)[/tex]
Distribute the 7.
[tex]C=14\pi[/tex]
To find one-fifth of the distance (formally termed the circumference) around the circle, divide the circumference by 5.
[tex]\displaystyle \frac{14\pi}{5}[/tex]
If you are looking for a simplified answer in terms of π, this will suffice. If you need an exact answer that does not reference π, continue reading.
For a solution not in terms of π, first, multiply 14 by π.
[tex]14\times\pi = 43.98229715[/tex]
Divide this value by 5.
[tex]\displaystyle \frac{43.98229715}{5} = 8.7964594[/tex]
To make this easier to present, round to the hundredths place.
[tex]8.7964594 \approx 8.80[/tex]
The final answer, dependent on the value you are asked to provide, is:
[tex]{\boxed{\displaystyle \frac{14\pi}{5} \ \text{inches}}[/tex]
[tex]\boxed{\text{approximately} \ 8.8 \ \text{inches}}[/tex]
