Circle Sector

Michael M

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Hi All
I am trying to calculate the segment area of a circle, but my unknown is the central angle.
As an example
A 500mm Dia circle with the bottom 30mm cut off....I need the area of the bottom 30mm, but, as I said , I don't have the central angle

I'd really appreciate anyones Geometry assistance, all I can find on the Net requires that central angle,
 

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Fazza

MrExcel MVP
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diameter 500
radius 250

looking at a cut-off point, radius 250, horizontal distance to centre is 220

so angle from 'vertical' to cut off point has side 220 & hypotenuse 250

or cosine angle = 220/250

OK?
 

Michael M

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Hi Fazza
Did I mention my complete and utter inability to understand geometry....LOL !!

So, the answer you gave me was the Cosine of the central angle ??
 

Fazza

MrExcel MVP
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actually half of the subtended angle

a little sketch will show it. remember that the radius is 250 and the cut off of 30 gives the 220...
 

Michael M

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Thanks Fazza
I have a sketch...I'll try and make some sense of the maths
I have been looking at another way by calculating the chord length and then the area of the 2 triangles, which apparently is accurate to within 0.3%, which is more than adequate.
 

sulakvea

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sry - will get back shortly
 
Last edited:

Michael M

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Fazza, yep been there....but i think I'll run with the Chord length method.
Really appreciate the input though....out here in the bush, we just clap hands to find the central angle....LOL !!

Sulakvea
Thanks for the input....but I don't have the central angle...as I said, I'll go with the chord method for a suitable degree of accuracy
 

sulakvea

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hi Michael, sorry for the previous post - made a mistake in calculations and knew wouldnt let me edit by the time i fixed it. here it is:

the formula is (R^2) /2 * (Angle - Sin (Angle))

just like Fazza suggested - cos() of the half angle would be 220/250. sin() of the same half angle would be 1-cos() = 1-22/25 = 3/25 = 0.12

you need the angle (i.e. Arcsin).

Arcsin(X) = Atn(X / Sqr(-X * X + 1)) (from VBA help), plug in 0.12 and you get 0.120289882394788. times 2 = 0.240579765.

plug in the numbers. you get (250^2)*2 / (0.240579765-0.12)

HTH
 

Michael M

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Thanks again
I am going to try the formulae and see how much difference there really is between the 2.
But if I can get within 0.5%, I will be more than happy
 

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