Question

Find the distance around one-fifth of a circle with diameter of 14 inches

Answer 1

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.

Find the Circumference

The circumference of a circle is found using the formula C = 2πr.

$C = 2\pi r$

We are given the diameter. The radius can be found using r = D/2.

$\displaystyle r=\frac{D}{2}$

$\displaystyle r=\frac{14}{2}$

$r=7$

Plug in the radius to the formula for a circle's circumference: C = 2πr.

$C = 2 \pi (7)$

Rearrange the equation to distribute the 7 into the 2π.

$C = 7(2\pi)$

Distribute the 7.

$C=14\pi$

Find One-Fifth of the Distance

To find one-fifth of the distance (formally termed the circumference) around the circle, divide the circumference by 5.

$\displaystyle \frac{14\pi}{5}$

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.

$14\times\pi = 43.98229715$

Divide this value by 5.

$\displaystyle \frac{43.98229715}{5} = 8.7964594$

To make this easier to present, round to the hundredths place.

$8.7964594 \approx 8.80$

The final answer, dependent on the value you are asked to provide, is:

${\boxed{\displaystyle \frac{14\pi}{5} \ \text{inches}}$

$\boxed{\text{approximately} \ 8.8 \ \text{inches}}$