Question

find the length of the arc shown in red. Leave your answer in terms of pie

Answer 1

EXPLANATION

Given the circle, we can see the following facts:

Diameter= 24 ft ----> radius= 12 ft

Total arc length = 360°

The arc of a semi-circle is equal to 360/2 = 180 degrees

The red labeled arc is given by the difference between 360, the other 60 degrees and the semi-circle,

360° - 180° - 60° = 120°

So, representing this as a radian form:

$\text{arc length = 2}\cdot\pi\cdot r\cdot(\frac{\theta}{360})$$\text{arc length = 2}\cdot\pi\cdot12\cdot(\frac{120}{360})$

Multiplying terms:

$\text{arc length = 24}\cdot\pi\cdot\frac{1}{3}$

Simplifying:

$\text{arc length= 8}\cdot\pi$

So, the answer is 8π ft