Question

What is the approximate length of the arc su tended by an angle 4pie/3 radians on a circle with a radius of 6.00 meters?

Answer 1

$\bf \textit{arc's length}\\\\ s=r\theta \quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ r=6\\ \theta =\frac{4\pi }{3} \end{cases}\implies s=6\cdot \cfrac{4\pi }{3}\implies s=8\pi$

Answer 2

We will see that the length of the arc is 25.12 m.

We know that for a circle of radius R, the circumference is:

C = 2*pi*R

Where pi = 3.14

If we only take a section of the circle defined by the angle θ, the length of the arc of that section is just:

L = θ*R

Here we have:

θ = (4/3)*pi

R = 6.0 m

Then we replace that in the above equation:

L =  (4/3)*pi*6.0m = (4/3)*3.14*6.0m = 25.12 m.

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