You are watching: 1/3 of a circle
You are describing a circular segment who area is (1 /3 )r2 , yet I doubt you currently know that.
The area of a one segment have the right to be deduced native the area the the one sector and also the area of the isosceles triangle within the circular sector. This chart helps describe things:
Thus, you desire to deal with (1 /3 )r2 = ½r2(-sin), i m sorry simplifies come 3 - 3sin - 2 = 0. Note that the angle is the central angle measure in radians.
This equation is not basic to solve. In fact, the easiest approach is to fix it numerically (that is, to discover a close approximation).
Using a spreadsheet package, i calculated an approximation the f() = 3 - 3sin - 2.
Clearly, have to be in between zero and also radians, so using those together the initial boundaries, ns quickly split the selection of feasible values the in fifty percent and zeroed in top top the approximate worth of that answers her question.
The length of the chord can be calculated given the radius r and also this angle
so sin( / 2) = (c / 2) / r.
Hope this helps, Stephen La Rocque.
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