Question
The area of a segment of a circle is 330 square meter. If the longest chord of the segment is 57 meter,find its radius.
Answers
Steve
recall that the area of a segment is
a = 1/2 r^2 (θ-sinθ)
If the longest chord is c, then
(c/2)/r = sin(θ/2)
So, now we have
27.5 = r*sin(θ/2)
330 = 1/2 r^2 (θ-sinθ)
Solve those two and you have
θ = 1.24
so, r = 47.33
as always, check my math
a = 1/2 r^2 (θ-sinθ)
If the longest chord is c, then
(c/2)/r = sin(θ/2)
So, now we have
27.5 = r*sin(θ/2)
330 = 1/2 r^2 (θ-sinθ)
Solve those two and you have
θ = 1.24
so, r = 47.33
as always, check my math