# Math Help - Urgent angles

1. ## Urgent angles

1.The length of the arc of the sector is 12 pie. Find the length of the radius r.

2. The area of the sector is 18 pie cm $^2$ (squared). Find the length of the radius r.

2. 1) Use the formula they gave you for the arc length s having radius r and subtending angle a: s = ra. Assuming "pie" really means "pi" (or $\pi$), plug in "12pi" for "s" and "30 degrees" for "a". Solve for "r".

2) A length cannot have squared units. Did they perhaps actually give you the area of the sector, rather than the length of the arc?

If so, then use the formula they gave you for the area A of the sector having radius r and subtending angle a: A = (a/2)(r^2). Plug "18pi" in for "A" and "45 degrees" in for "a". Solve for "r".

If you get stuck, please reply showing how far you have gotten. Thank you!

3. so would it be for question one 12 pi divided by 30 = r? ----------------------------- i.e ------ s = r x a is 12pi=r x 30

12 pi /30 = 1.25663706

Is This Correct ?

4. 2)
A(abc)=18 pi
18pi=(n.r^2.45)/360
144=r^2
r=12
squared what you mean i dont understand if you mean this..solution this.
if it is something different so..

5. Originally Posted by Apocalypse
1.The length of the arc of the sector is 12 pie. Find the length of the radius r.
Hi Apocalypse,

We can do this a couple of ways. The general formula for finding an arc length given a central angle and radius is

$s=\theta r$, where s = the arc length, $\theta$= the measure of the central angle in radians, and r = the length of the radius.

$12\pi = \frac{\pi}{6}\cdot r$

Solve for r.

Another approach would be to determine what part of 360 degrees is 30 degrees. Then multiply that times the circumference to get the arc length of $12 pi$.

$\frac{30}{360}\cdot 2 \pi r=12 \pi$. You should arrive at the same solution for r.

Originally Posted by Apocalypse
2. The area of the sector is 18 pie cm $^2$ (squared). Find the length of the radius r.
For this one, I would find what part of the circle 45 degrees is, and then multiply that times the area of a circle to get the area of the sector. Then, from that equation, solve for r.

$\frac{45}{360}\cdot \pi r^2=18 \pi$

..

6. Originally Posted by Apocalypse
so would it be for question one 12 pi divided by 30 = r? ----------------------------- i.e ------ s = r x a is 12pi=r x 30

12 pi /30 = 1.25663706

Is This Correct ?
$s = r \cdot \theta$ is valid for $\theta$ in radians, not degrees.