Question

A. 8pi B. pi C. 2pi D. 4pi

Answer 1

Answer: Option C

$AC = 2\pi$

Step-by-step explanation:

The arc length is calculated as

$L = \theta * R$

Then

$AC = \theta * R$

We know that

$BC = 24\ ft$

If BC is the diameter of the circumference then the radius R is:

$R = \frac{BC}{2}$

$R = \frac{24}{2}$

$R = 12\ ft$

Now we convert the anglo from degrees to radians$\theta= 30\° * \frac{\pi}{180\°}\\\\\theta=\frac{1}{6}\pi$

Finally

$AC = \frac{1}{6}\pi * 12$

$AC = 2\pi$

Answer 2

Answer:

The length of the arc AC is 2π ⇒ answer C

Step-by-step explanation:

* Lets revise some facts in the circle

- The length of the arc is depends on the measure of the arc and the

  radius of the circle

- The length of the arc is a part of the length of the circle

- The length of the circle is 2πr

- The rule of the length of the arc = $\frac{\alpha }{360}*2\pi r$,

  where α is the measure of the arc

* Now lets solve the problem

- In circle P

∵ BC is a diameter

∵ BC = 24 ft

∵ The length of the radius of the circle is 1/2 the length of the diameter

∴ The length of the radius = 1/2 × 24 = 12 ft

- Ac is an arc in the circle

∵ The measure of the arc = 30°

∵ The length of the arc = $\frac{\alpha }{360}*2\pi r$ ,

  where α is the measure of the arc

∴ α = 30°

∵ r = 12 ft

∴ The length of the arc = $\frac{30}{360}*2(12)\pi=\frac{1}{12}*(24)\pi=2\pi$

∴ The length of the arc AC is 2π