Question

A circle has a radius of 6. An arc in this circle has a central angle of 48degrees. What is the length of the arc?

Answer 1

Answer:

The length of the arc:

$A = \frac{8}{5} \pi$

Step-by-step explanation:

To find the length of the arc< you need this equation:

$Arclength = \frac{a}{360\textdegree} 2\pi r$

-Use the given radius $6$ and the central angle $48\textdegree$ for the equation:

$A = \frac{48\textdegree}{360\textdegree} 2\pi (6)$

Then, solve the equation:

$A = \frac{48\textdegree}{360\textdegree} 2\pi (6)$

$A = \frac{2}{15} \times 2\pi \times 6$

$A = \frac{4}{15} \pi \times 6$

$A = \frac{24}{15} \pi$

$A = \frac{8}{5} \pi$

So, the length of the arc is $\frac{8}{5} \pi$ .