Question

HELP PLEASEEE 35 POINTS

Various circular targets are used by archery students. Daryl is using a target with an area of 36π square inches. What is the circumference of this target? Explain how you found your answer, and show your work. Express your answer in terms of π .

Answer 1

We have been given that various circular targets are used by archery students. Daryl is using a target with an area of 36π square inches. We are asked to find the circumference of the target.

To find the circumference of the target, we will use area of circle and circumference of circle formulas.

We know that area of circle is
`\pi r^2` and circumference of circle is
`2\pi r`, where r represents radius of circle in both formulas.

First of all, we will equate area formula with given area of target and solve for r as:

`\pi r^2=36\pi`

`(\pi r^2)/(\pi)=(36\pi)/(\pi)`

`r^2=36`

Now we will take positive square root as:

`√(r^2)=√(36)`

`r=6`

Therefore, radius of circle is 6.

Now we will substitute
`r=6` in circumference of circle formula.

`\text{Circumference}=2\pi r\Rightarrow 2\pi (6) =12\pi`

Therefore, the circumference of target is
`12\pi`.