Question

The radius of a circle is 9 inches. What is the length of a 45° arc?

Answer 1

SOLUTION:

Step 1:

In this question, we are given the following:

The radius of a circle is 9 inches.

What is the length of a 45° arc?

Step 2:

The details of the solution are as follows:

$\begin{gathered} Arc\text{ length = }\frac{\theta}{360^0}\text{ x 2}\pi r \\ where\text{ }\theta\text{ = 45}^0 \\ Radius\text{ = 9 inches} \\ \end{gathered}$$\begin{gathered} Arc\text{ length =}\frac{45^0}{360^0}\text{ x 2 x }\pi\text{ x 9} \\ =\frac{1}{8}\text{ x 2 x }\pi\text{ x 9} \\ =\text{ }\frac{18\pi}{8} \\ =\text{ }\frac{9\pi}{4} \\ =\text{ 7.068583471} \\ \approx\text{ 7.07 inches \lparen correct to 2 decimal places\rparen} \end{gathered}$

CONCLUSION:

The length of the Arc = 7.07 inches ( correct to 2 decimal places )