Question

The arc length of the semicircle shown in green is 34. What is the radius of the circle? R=

Answer 1

Given:

`\begin{gathered} \text{length of arc = 32}\pi \\ \theta=180^0(angle\text{ on a straight line or angle in semi circle)} \\ r=\text{?} \end{gathered}`

To calculate the length of an arc, the formula is;

`\begin{gathered} l=(\theta)/(360)*2\pi r \\ \text{Substituting all the parameters into the formula;} \\ 32\pi=(180)/(360)*2\pi r \\ 32\pi=\frac{360\pi\text{ r}}{360} \\ 32\pi=\pi r \\ r=(32\pi)/(\pi) \\ r=32 \end{gathered}`

Therefore, the radius of the circle 32 units.