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Find the area of the shaded region. Point O marks the center of the circle. Picture below!
I need someone to give me the equation to follow to solve the problem please!
 one year ago
 one year ago
Find the area of the shaded region. Point O marks the center of the circle. Picture below! I need someone to give me the equation to follow to solve the problem please!
 one year ago
 one year ago

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ConfusedFreshyBest ResponseYou've already chosen the best response.0
dw:1344217058690:dw
 one year ago

shadowfiendBest ResponseYou've already chosen the best response.1
Is the entire circle shaded?
 one year ago

ConfusedFreshyBest ResponseYou've already chosen the best response.0
No the right hand corner arc is not. That is kind of hard to see but it is not shaded up there.
 one year ago

shadowfiendBest ResponseYou've already chosen the best response.1
Got it. And what's the 90 degrees?
 one year ago

ConfusedFreshyBest ResponseYou've already chosen the best response.0
I believe it is the central angle.
 one year ago

shadowfiendBest ResponseYou've already chosen the best response.1
Hm. I feel like I still don't have a good grasp of what the image looks like. Is there any chance you could either take a picture of it and upload it or draw it in a tool that can do the shading a little better and upload that image? We know our drawing tool needs a bit of work :/
 one year ago

ConfusedFreshyBest ResponseYou've already chosen the best response.0
dw:1344217343489:dw
 one year ago

ConfusedFreshyBest ResponseYou've already chosen the best response.0
Is that better?
 one year ago

shadowfiendBest ResponseYou've already chosen the best response.1
Definitely, though the 90 degrees still seems somewhat unrelated to anything in the drawing…
 one year ago

ConfusedFreshyBest ResponseYou've already chosen the best response.0
I think the central angle is supposed to be 90 degrees. That is why it is there.
 one year ago

shadowfiendBest ResponseYou've already chosen the best response.1
Meaning the angle formed by the two endpoints of the chord and the center, yes?
 one year ago

shadowfiendBest ResponseYou've already chosen the best response.1
Ok, then I think what you can do is, because it's a 90 degree angle you know that the circle portion in question is 1/4 the circle, right?
 one year ago

ConfusedFreshyBest ResponseYou've already chosen the best response.0
Yes I know that.
 one year ago

shadowfiendBest ResponseYou've already chosen the best response.1
And in order for that to be true, what does the length of the line segment from the center of the circle to the endpoint of the chord have to be?
 one year ago

ConfusedFreshyBest ResponseYou've already chosen the best response.0
4, since the radius is 4.
 one year ago

shadowfiendBest ResponseYou've already chosen the best response.1
Precisely. Can you get the area of that sector of the circle, ignoring the chord?
 one year ago

ConfusedFreshyBest ResponseYou've already chosen the best response.0
What I got could not be correct.
 one year ago

ConfusedFreshyBest ResponseYou've already chosen the best response.0
I got 720. Seeing that the formula for area of a sector is Area= [angle]radius^2/ 2
 one year ago

shadowfiendBest ResponseYou've already chosen the best response.1
I'll leave aside whether that formula is correct or not, in this particular case we've already determined that this is a quarter of the circle, so really it's just area / 4, right?
 one year ago

ConfusedFreshyBest ResponseYou've already chosen the best response.0
Yes. Which would equal 180?
 one year ago

shadowfiendBest ResponseYou've already chosen the best response.1
Well, area is pi * r^2, which here is pi * 4^2, which is pi * 16 right?
 one year ago

ConfusedFreshyBest ResponseYou've already chosen the best response.0
Yes. That divided by 4 is 4.
 one year ago

shadowfiendBest ResponseYou've already chosen the best response.1
Right, so we have pi * 4, which is ~12.566
 one year ago

ConfusedFreshyBest ResponseYou've already chosen the best response.0
What does that mean? Is that the area of the whole sector?
 one year ago

shadowfiendBest ResponseYou've already chosen the best response.1
Correct. So now let's figure out the area of the *unshaded* portion of the sector.
 one year ago

shadowfiendBest ResponseYou've already chosen the best response.1
We can do that by finding the area of the triangle formed by the central angle and the chord, right?
 one year ago

ConfusedFreshyBest ResponseYou've already chosen the best response.0
Ummm. Pythagorean theorem so it could be 32= c^2
 one year ago

shadowfiendBest ResponseYou've already chosen the best response.1
Well, that's how you'd find the length of the chord. We're just interested in the area of this: dw:1344218326720:dw
 one year ago

ConfusedFreshyBest ResponseYou've already chosen the best response.0
Omg. I just derped so hard there. The base and height of the triangle is 4 and 4. so it would be 8?
 one year ago

shadowfiendBest ResponseYou've already chosen the best response.1
Exactly! So, how do we get the area of the unshaded area of that sector?
 one year ago

ConfusedFreshyBest ResponseYou've already chosen the best response.0
12.566 minus 8. 4.566 is the unshaded area?
 one year ago

shadowfiendBest ResponseYou've already chosen the best response.1
Yep. And now the area of the shaded part of the circle?
 one year ago

ConfusedFreshyBest ResponseYou've already chosen the best response.0
You just lost me again. Which part am I looking for? THe rest of the circle?
 one year ago

shadowfiendBest ResponseYou've already chosen the best response.1
Yeah, the shaded area of the circle is everything except the unshaded part we just found the area of right?
 one year ago

ConfusedFreshyBest ResponseYou've already chosen the best response.0
I seriously do not know. I feel so stupid whenever I do geometry. Is it 8?
 one year ago

shadowfiendBest ResponseYou've already chosen the best response.1
Well, it's going to be pi*r^2 of the circle  the area we just calculated. Do you see how that works?
 one year ago

shadowfiendBest ResponseYou've already chosen the best response.1
Basically, to find the area of the circle except for that portion, we worked backwards to find the area of that portion, then subtract it from the area of the circle as a whole.
 one year ago

shadowfiendBest ResponseYou've already chosen the best response.1
Sounds about right!
 one year ago

ConfusedFreshyBest ResponseYou've already chosen the best response.0
Thank you so much!!
 one year ago

shadowfiendBest ResponseYou've already chosen the best response.1
No problem! Hope that helped the reasoning for other problems!
 one year ago
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