# What is the arc length of a semicircle if the diameter is 10?

Mar 19, 2018

$15.71$

#### Explanation:

The arc length of a circle has it's own formula:

${m}^{\circ} / \left({360}^{\circ}\right) \pi d$

${m}^{\circ} = \text{angle measure of arc}$
$d = \text{diameter}$

Since this is a $\text{semicircle}$, the angle measure of the arc is going to be ${180}^{\circ}$. And they said that the diameter is $10$, so we can update the formula:

$\frac{m}{360} \pi d$

$\frac{180}{360} \pi \left(10\right)$

$0.5 \pi 10$

$5 \pi$

Use your calculator to find the value of $5 \pi$ or use the number $3.1415927$ for $\pi$ if you have to do it manually.

$5 \pi = 15.71$

So the arc measure of the semi circle is $15.71$