Question

What is the length of AC if the circumference is 36?

Answer 1

Explanation:

The answer should be 9

Answer 2

9 units

1) If the Circumference is 36 then we can find the radius.

`\begin{gathered} C=2\pi R \\ 36=2\pi R \\ (36)/(2\pi)=\frac{2\pi\cdot R}{{2\pi}}\frac{}{} \\ R=(18)/(\pi) \end{gathered}`

2) Now we can find the length of that arc AC, using this formula and plugging the radius:

`\begin{gathered} l=(\alpha)/(360)\cdot2\pi\cdot r \\ l=(90)/(360)\cdot2\pi\cdot(18)/(\pi) \\ l=(1)/(4)\cdot36 \\ l=9 \end{gathered}`

3) Hence, the length of that arc AC is 9 units