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 2 years 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!
 2 years 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!

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ConfusedFreshy
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1344217058690:dw

shadowfiend
 2 years ago
Best ResponseYou've already chosen the best response.1Is the entire circle shaded?

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

shadowfiend
 2 years ago
Best ResponseYou've already chosen the best response.1Got it. And what's the 90 degrees?

ConfusedFreshy
 2 years ago
Best ResponseYou've already chosen the best response.0I believe it is the central angle.

shadowfiend
 2 years ago
Best ResponseYou've already chosen the best response.1Hm. 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 :/

ConfusedFreshy
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1344217343489:dw

shadowfiend
 2 years ago
Best ResponseYou've already chosen the best response.1Definitely, though the 90 degrees still seems somewhat unrelated to anything in the drawing…

ConfusedFreshy
 2 years ago
Best ResponseYou've already chosen the best response.0I think the central angle is supposed to be 90 degrees. That is why it is there.

shadowfiend
 2 years ago
Best ResponseYou've already chosen the best response.1Meaning the angle formed by the two endpoints of the chord and the center, yes?

shadowfiend
 2 years ago
Best ResponseYou've already chosen the best response.1Ok, 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?

ConfusedFreshy
 2 years ago
Best ResponseYou've already chosen the best response.0Yes I know that.

shadowfiend
 2 years ago
Best ResponseYou've already chosen the best response.1And 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?

ConfusedFreshy
 2 years ago
Best ResponseYou've already chosen the best response.04, since the radius is 4.

shadowfiend
 2 years ago
Best ResponseYou've already chosen the best response.1Precisely. Can you get the area of that sector of the circle, ignoring the chord?

ConfusedFreshy
 2 years ago
Best ResponseYou've already chosen the best response.0What I got could not be correct.

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

shadowfiend
 2 years ago
Best ResponseYou've already chosen the best response.1I'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?

ConfusedFreshy
 2 years ago
Best ResponseYou've already chosen the best response.0Yes. Which would equal 180?

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

ConfusedFreshy
 2 years ago
Best ResponseYou've already chosen the best response.0Yes. That divided by 4 is 4.

shadowfiend
 2 years ago
Best ResponseYou've already chosen the best response.1Right, so we have pi * 4, which is ~12.566

ConfusedFreshy
 2 years ago
Best ResponseYou've already chosen the best response.0What does that mean? Is that the area of the whole sector?

shadowfiend
 2 years ago
Best ResponseYou've already chosen the best response.1Correct. So now let's figure out the area of the *unshaded* portion of the sector.

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

ConfusedFreshy
 2 years ago
Best ResponseYou've already chosen the best response.0Ummm. Pythagorean theorem so it could be 32= c^2

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

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

shadowfiend
 2 years ago
Best ResponseYou've already chosen the best response.1Exactly! So, how do we get the area of the unshaded area of that sector?

ConfusedFreshy
 2 years ago
Best ResponseYou've already chosen the best response.012.566 minus 8. 4.566 is the unshaded area?

shadowfiend
 2 years ago
Best ResponseYou've already chosen the best response.1Yep. And now the area of the shaded part of the circle?

ConfusedFreshy
 2 years ago
Best ResponseYou've already chosen the best response.0You just lost me again. Which part am I looking for? THe rest of the circle?

shadowfiend
 2 years ago
Best ResponseYou've already chosen the best response.1Yeah, the shaded area of the circle is everything except the unshaded part we just found the area of right?

ConfusedFreshy
 2 years ago
Best ResponseYou've already chosen the best response.0I seriously do not know. I feel so stupid whenever I do geometry. Is it 8?

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

shadowfiend
 2 years ago
Best ResponseYou've already chosen the best response.1Basically, 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.

shadowfiend
 2 years ago
Best ResponseYou've already chosen the best response.1Sounds about right!

ConfusedFreshy
 2 years ago
Best ResponseYou've already chosen the best response.0Thank you so much!!

shadowfiend
 2 years ago
Best ResponseYou've already chosen the best response.1No problem! Hope that helped the reasoning for other problems!
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