#Need help with circle segments

63 messages · Page 1 of 1 (latest)

idle osprey
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i need the area of the blue-purple and purple-green curved sections

image.png
median belfryBOT
idle osprey
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the radius of the circle is 8u, the curved blue line is of a circle with a radius of 8(sqrt2), translated so it hits the origin

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the area of those 2 poorly highlighted sections together is ~84.4u

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i put those purple lines to try and find the area of one of the sectors, which turned out to be 32u^2 (major sector) but i feel that it is wrong

bright garden
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of AC right?

idle osprey
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i was trying to find the area of the sector but i got confused and got 32, which doesnt seem realistic

idle osprey
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i have the area of the blue green piece so i just need one of those for my 2 pieces

bright garden
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u can get traingle ABC

idle osprey
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i have angle abc, do i need the area?

bright garden
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so this is sector area ^

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this is trainglearea ^

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do u think we can use these two to find out the answer?

idle osprey
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yes, area(sector)-area(triangle), but i had trouble with area of sector

bright garden
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well a circle has 360 degrees right?

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if u have 180 degrees the circle area would be half

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and 90 would be 1/4

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because angle represents how much of the total area of the circle u have

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so we use R to get the total area of the sircle

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then divide it to how much of the circle we want

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(whichis given bythe angle)

bright garden
idle osprey
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i understand how to get it, ty, but dont understand the area of a sector formula. could you please tell me the formula

bright garden
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so lets say we have a circle with 360

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its area is just well the formula for the area of the circle

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pi X r^2

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makes sense so far right?

idle osprey
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uh ok

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assuming theta is ABC right

bright garden
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so we can divide the circe into 360 equal (sectors) where each sector gets 1/360 of the total area

bright garden
idle osprey
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ohhh ty

bright garden
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does the sector formula make sense now?

idle osprey
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oh

bright garden
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this is why 90 gives u 1/4 of the total area

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and 180 gives you 1/2

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it is litterly cutting the circle into smaller parts-

idle osprey
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so ABC, 158, would give me the area then

bright garden
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so angle ABC/360 x (Area of circle)

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is = the sector area

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then we jsut get area of traingle ABC

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and we have can just remove traingle area from sector

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makes sense?

idle osprey
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tysm

bright garden
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np!

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also u can think of the second one like this!

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andwith the same idea with the first one we can also get the answer of the (yellow area)

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does that make sense??

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lmk if u need anything else!! catlove

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goodluckkk!! and if u solve it dont forget to do .solved!!

bright garden
idle osprey
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anyways, ty again

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.solved