Lethal
Geometry question w/ a Circle. find area of a shaded region. (Harder problem)
Delete
Share
This Question is Closed
Lethal
Best Response
You've already chosen the best response.
0
|dw:1345779977023:dw|
Lethal
Best Response
You've already chosen the best response.
0
I think what you have to do is to bisect the triangle into 60 degree up top and then the bottom left and right are still 30 degrees. then you do the 30 60 90 triangle thing.
Lethal
Best Response
You've already chosen the best response.
0
i am stuck from there
alexwee123
Best Response
You've already chosen the best response.
1
i did it a different way...
Lethal
Best Response
You've already chosen the best response.
0
well explain.
alexwee123
Best Response
You've already chosen the best response.
1
with integrals...
Lethal
Best Response
You've already chosen the best response.
0
well. it shouldn't be that complicated im only doing geometry.
Mimi_x3
Best Response
You've already chosen the best response.
1
Area of minor segment \[A = \frac{1}{2} r^2 \left(\theta-\sin\theta\right) \]
But the only problem is \(r\) is not given..
Hero
Best Response
You've already chosen the best response.
0
I think I meant to post the area of a sector of a circle
Lethal
Best Response
You've already chosen the best response.
0
you guys are thinking too hard its only like subtracting a sector
Mimi_x3
Best Response
You've already chosen the best response.
1
Area of sector - area of triangle
Hero
Best Response
You've already chosen the best response.
0
Yeah that
Mimi_x3
Best Response
You've already chosen the best response.
1
But \(r\) is not given!!!
Im thinking of using the cosine rule and sine rule to find \(r\) would it work?
Lethal
Best Response
You've already chosen the best response.
0
here ill take it a bit further.
|dw:1345780578744:dw|
does that help?
Hero
Best Response
You've already chosen the best response.
0
It will not be hard to find \(r\)
Hero
Best Response
You've already chosen the best response.
0
Is the vertex of angle 120 is the center of the circle?
Lethal
Best Response
You've already chosen the best response.
0
yep
Mimi_x3
Best Response
You've already chosen the best response.
1
|dw:1345780720301:dw|
looks like you can use the sine rule..
Hero
Best Response
You've already chosen the best response.
0
Okay, so yeah just do
Area of Sector - Area of Triangle like what @Mimi_x3 suggested
Lethal
Best Response
You've already chosen the best response.
0
soo all we need is the area of the circle and then we can use the 120/360 * pi r2 or something and subtract the area from that.
Mimi_x3
Best Response
You've already chosen the best response.
1
lets find \(r\) first
Lethal
Best Response
You've already chosen the best response.
0
|dw:1345780842471:dw|
Mimi_x3
Best Response
You've already chosen the best response.
1
I got 8 as well using the sine rule
Mimi_x3
Best Response
You've already chosen the best response.
1
Now its easy..you can do it yourself
Lethal
Best Response
You've already chosen the best response.
0
ok so 64 pi is the area of the circle
Lethal
Best Response
You've already chosen the best response.
0
and the area of the triangle left side is 1/2 * 4sqroot3 * 4
Lethal
Best Response
You've already chosen the best response.
0
*2 to make up for the other side.
Mimi_x3
Best Response
You've already chosen the best response.
1
I will just use this formula\[A = \frac{1}{2} r^2 \left(\theta-\sin\theta\right) \]
No need to derive it
Lethal
Best Response
You've already chosen the best response.
0
ok
Mimi_x3
Best Response
You've already chosen the best response.
1
and it must be in radians..so convert it..
Lethal
Best Response
You've already chosen the best response.
0
oh heck nah jose
alexwee123
Best Response
You've already chosen the best response.
1
you guys are thinking too hard o.0
Lethal
Best Response
You've already chosen the best response.
0
oh wait i got the answer. just do 120/360 which is 1/3
and then i did 1/3 * 64pi which is the area of the circle and it is
64pi/3 and now subtract it by the area of the triangle which is
Lethal
Best Response
You've already chosen the best response.
0
1/2 4sqrt3 * 4 or
8sqrt3 * 2 for the other side
alexwee123
Best Response
You've already chosen the best response.
1
|dw:1345781211630:dw|
|dw:1345781273195:dw|
alexwee123
Best Response
You've already chosen the best response.
1
|dw:1345781325118:dw|
Lethal
Best Response
You've already chosen the best response.
0
so the final answer is \[64\pi/3 - 16\sqrt{3}\]
alexwee123
Best Response
You've already chosen the best response.
1
yes good job @Lethal
Lethal
Best Response
You've already chosen the best response.
0
yep, i would best response both of u but i can only do one. thx alex.