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ksaimouli Group TitleBest ResponseYou've already chosen the best response.0
dw:1358806909531:dw
 one year ago

ksaimouli Group TitleBest ResponseYou've already chosen the best response.0
area of circle
 one year ago

ksaimouli Group TitleBest ResponseYou've already chosen the best response.0
@zepdrix
 one year ago

Outkast3r09 Group TitleBest ResponseYou've already chosen the best response.0
what are you trying to find
 one year ago

ksaimouli Group TitleBest ResponseYou've already chosen the best response.0
area of that
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
dw:1358880151258:dwYour picture is so sloppy :D Lemme see if this looks correct.
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
Theta is the angle. s is the letter we use for arc length.
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
Umm let's first find the radius. I think we're going to need that. Here is a helpful formula:\[\large s=r \theta\]We want to solve for r so let's divide both sides by \(\theta\).\[\large \frac{s}{\theta}=r\]
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
Our theta is given in degrees, so we'll need to convert it to radians.\[\large 30^o \left(\frac{\pi}{180^o}\right)=\frac{\pi}{6}\] So our radius is given by this,\[\large r=\frac{6\pi}{\left(\dfrac{\pi}{6}\right)}\] Which tells us that we have a radius of 36.
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
So now we need the area of this sector. Hmm. So it's a percentage of the area of a circle. So it will end up being the same formula we use for area of a circle, just with a fraction in front of it to show that we only want a fraction of that area.\[\large A=\left(C\right)\pi r^2\]From here we just need to find out what C is. You actually probably have a formula on a sheet somewhere, so I likely don't need to go into this much detail :) lol my bad. Anyway, our fraction will be the number of degrees we care about DIVIDED BY the total degrees in a circle.\[\large A=\left(\frac{30^o}{180^o}\right)\pi r^2\]The degree bubbles will cancel out, giving us a unitless quantity (which is what we want).\[\large A=\left(\frac{1}{6}\right)\pi r^2\]
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
And we determined earlier that our radius was \(\large r=36\). Plugging this in gives us,\[\large A=\left(\frac{1}{6}\right)\pi (36)^2 \qquad = \qquad \left(\frac{1}{\cancel{6}}\right)\pi (6)^{\cancel{4}3}\]
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
\[\large A=216\pi\]
 one year ago
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