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$\displaystyle ^2$ (squared). Find the length of the radius r.
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 $\displaystyle \pi$), 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!
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
$\displaystyle s=\theta r$, where s = the arc length, $\displaystyle \theta$= the measure of the central angle in radians, and r = the length of the radius.
$\displaystyle 12\pi = \frac{\pi}{6}\cdot r$
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 $\displaystyle 12 pi$.
$\displaystyle \frac{30}{360}\cdot 2 \pi r=12 \pi$. You should arrive at the same solution for 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.
$\displaystyle \frac{45}{360}\cdot \pi r^2=18 \pi$
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