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=(D)/(2)`

`\displaystyle r=(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 (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*\pi = 43.98229715`

Divide this value by 5.

`\displaystyle (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 (14\pi)/(5) \ \text{inches}}`

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