Question

The question says “In the circle below, segment AB is a diameter. If the length of arc ACB is 6 *pie* what is the length of the radius of the circle

Answer 1

Solution

Given length or arc = 6π

The formula for length of arc is

$\begin{gathered} L_{Arc}=\frac{\theta}{360}\times2\pi r \\ \\ \text{ since }L_{Arc}=6\pi \\ \\ \theta=180 \end{gathered}$$\begin{gathered} \Rightarrow6\pi=\frac{180}{360}\times2\pi r \\ \\ \Rightarrow r=\frac{6\pi\times360}{180\times2\pi}=6 \end{gathered}$

Hence, the length of the radius is 6 units