Question

A circle has a circumference of 5. An arc in the circle has a central angle of 162°. What is the length of the arc?

Answer 1

Answer:

The length of the arc is 2.25 units.

Step-by-step explanation:

The circumference of a circle is $2\pi r$, where r is radius of the circle.

Total angle of a circle in degree is 360°.

Length of central angle formula

$\textrm{Arc length}=\frac{2\pi r}{360^\circ}\times \textrm{central angle degree}$

$\Rightarrow \textrm{Arc length}=\frac{\textrm{circumference}}{360^\circ}\times \textrm{central angle degree}$

Given that,

A circle has a circumference of 5 units.An arc in the circle has a central angle of 162°.

Then,

$\textrm{Arc length}=\frac{\textrm{circumference}}{360^\circ}\times \textrm{central angle degree}$

$\textrm{Arc length}=\frac{5}{360^\circ}\times162^\circ$

                 $=\frac{810}{360}$

                 $=\frac{9}{4}$

                 =2.25 units.

The length of the arc is 2.25 units.

Answer 2

Answer:

14.14 units

Step-by-step explanation:

Klan Academy - i checked and it was correct.