Question

Please help me

Please show all your work and round it your answer as needed.

1. Find the length of AB. Round it to the nearest hundredth.

Answer 1

Given that the radius of the circle is 6 cm.

The central angle is 120°

We need to determine the length of AB.

Length of AB:

The length of AB can be determined using the formula,

${arc \ length}=2 \pi r\left(\frac{\theta}{360}\right)$

where $\theta$ is the central angle and r is the radius of the circle.

Substituting $\theta=120$ and $r=6$ in the above formula, we get;

$arc\ length}=2 \pi (6)\left(\frac{120}{360}\right)$

Simplifying the values, we get;

$arc\ length}=2 \pi (6)\left(\frac{1}{3}\right)$

$arc\ length}=12 \pi \left(\frac{1}{3}\right)$

$arc\ length}=4 \pi$

Substituting π = 3.14, we have;

$arc\ length}=4(3.14)$

$arc\ length}=12.56$

Thus, the arc length of AB is 12.56 cm