Height and area of circular segment?
Height and area of circular segment
#1. Before somebody asks, this is NOT homework. This problem was inspired by working up ballistics data for 45 ACP ammo. Quickload Software indicated that powder ABC will only fill 67% of the straight-walled 45 ACP case ... which prompted this generalized question. Thanks.
- icemanLv 73 years agoFavorite Answer
The formula to find the area of the segment is given by:
½ R² (π/180 * θ − sinθ)
θ = the central angle in degrees
R = the radius of the circle
General formula for circle center to chord midpoint distance d:
d = √[(R² - (¼ C²)]
C = chord length
Note: let O be the center , OA & OB be the two radius R in the graph above, then the area in the green can also be found by calculating the area of the whole sector(pie shaped) and subtracting the area of the isosceles triangle △OAB.
Segment height h:
h = R - d
Area of the segment can also be calculated if h is known as follow:
Area = R² * arccos[(R - h)/R] - (R - h) * √(2Rh - h²)
I hope this helps.