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

Step-by-step explanation:

The length of an arc is given by the formula,

`\begin{gathered} Arc\text{ length = }(\theta)/(360)\text{ }*\text{ 2}\pi r \\ \end{gathered}`

Substituting the values in the formula,

`\begin{gathered} 14\pi\text{ = }(60)/(360)\text{ }*\text{ 2}*\pi* r \\ r\text{ = }(14*360)/(60*2) \\ r\text{ = }(5040)/(120) \\ r\text{ = 42} \end{gathered}`

Answer:

Thus the radius of the circle is 42 m.