Question

Find the length of the arc on a circle of radius r intercepted by a central angle ∅. 5. Radius, r = 12 inches Central Angle, ∅ = 45°

Answer 1

We are asked to find the length of the arc on a circle

Radius = r = 12 inches

Central Angle = θ = 45°​

The arc length on a circle is given by

`arc=2\cdot\pi\cdot r((\theta)/(360\degree))`

Let us substitute the given values of r and θ

`\begin{gathered} arc=2\cdot\pi\cdot r((\theta)/(360\degree)) \\ arc=2\cdot\pi\cdot12((45\degree)/(360\degree)) \\ arc=24\cdot\pi((1\degree)/(8\degree)) \\ arc=(24\cdot\pi)/(8) \\ arc=3\pi \end{gathered}`

Therefore, the arc length is found to be 3π inches.