Question

A circle has a radius of 20 inches. Find the length of the arc intercepted by a central angle of 45°. Leave answers in terms of π.A. 5π/2 inchesB. 5π inchesC. 5 inchesD. 4π inches

Answer 1

`5\pi\text{ inches (option B)}`

Step-by-step explanation:

radius = 20 inches

angle = θ= 45°

We would apply length of an arc:

`length\text{ of an arc = }\frac{\theta}{360\text{ }}\text{ }*2\pi r`
`\begin{gathered} \text{length of the arc = }(45)/(360)*2*\pi*20 \\ =\text{ }(1)/(8)*\text{ 40}\pi \end{gathered}`

Since the options is in terms of π, the answer will be in that form

`\text{length of }arc\text{ = 5}\pi\text{ inches (option B)}`