There are two main "slices" of a circle: |

** Watch in highest quility possible**

To work out the area of the segment and sector you will use the formulas:

Area of Sector = ½ × (θ × π/180) × r

^{2}

*(when θ is in degrees)*

*Area of Segment = ½ × ( (θ × π/180) - sin θ) × r*

^{2}

*(when θ is in degrees)*

**So basically what we need is the angle of the "center" corner, and the radius of the circle the sector belongs too**

*Click to make bigger* |

What these formulas will look like in

**ICE**

*-*

*once you have the angle and raduis -*

**:**

Segment area:

*Click to make bigger* |

Sector area:

*Click to make bigger* |

So you will need to work out the lengths of the three sides of the triangle that fits inside the sector "pizza slice".

I did this by simple creating cluster centers on the last point of the three curves then getting the length between them....

*Click to make bigger* |

Here are the tree's for that...

*Click to make bigger* |

*Click to make bigger* |

*Click to make bigger* |

....then you can work out the angle of the center corner in the circle your sector is part of.

I used the standard law of cosines node for this one but here is the math formula:

cos A = (b

^{2}+ c

^{2}- a

^{2})/2bc

I used this law because I already had all three side lengths worked out, but never fear here is a link to other ways of working out you triangles if you have say one angle and two sides...

*Click to make bigger* |

*Click to make bigger* |

You can also work out the "arc length"

*- the blue line in the image below -*of your sector, by using the formula:

**L = (θ × π/180) × r**

*Click to make bigger* |

Here's that

**ICE**tree...

*Click to make bigger* |

And there you have it. If you ever need to work out how big a pizza slice is ..... now you can do it :)

*End*
## 3 comments:

thanks for sharing sue!

No problem :D

Do you have Einsteins reference material :)

Post a Comment