Question

in circle O the radius is 4ft and the measure of minor arc ab is 120 degrees find the length of minor arc ab to the nearest integer

Answer 1

Answer:

$8\:\text{ft}$

Step-by-step explanation:

The length of the arc is proportional to the degree measure it in encompasses. Since there are 360 degrees in a circle and the arc is 120 degrees, the arc's length will be $\frac{120}{360}=\frac{1}{3}$ of the circle's length (circumference).

The circumference of a circle is given by $2\pi r$, where $r$ is the radius of the circle. Therefore, the circumference of the circle is $2\pi(4)=8\pi$. As we found earlier, the length of the arc is $\frac{1}{3}$ of this circumference. Therefore, the arc's length is $8\pi\cdot \frac{1}{3}=\frac{8\pi}{3}$.

To the nearest integer, this is $\approx \boxed{8\:\text{ft}}$.