Question

Find the radius of the circle containing 60° arc of a circle whose length is 14 m.

Answer 1

Given:

It is given that

$\begin{gathered} \theta\text{ = 60}^0 \\ Arc\text{ length = 14}\pi \end{gathered}$

Required:

The radius of the circle

Explanation:

The length of an arc is given by the formula,

$\begin{gathered} Arc\text{ length = }\frac{\theta}{360}\text{ }\times\text{ 2}\pi r \\ \end{gathered}$

Substituting the values in the formula,

$\begin{gathered} 14\pi\text{ = }\frac{60}{360}\text{ }\times\text{ 2}\times\pi\times r \\ r\text{ = }\frac{14\times360}{60\times2} \\ r\text{ = }\frac{5040}{120} \\ r\text{ = 42} \end{gathered}$

Answer:

Thus the radius of the circle is 42 m.