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Minor arc AB in the diagram is 30 degrees and the radius of the circle is 16. Find the area of circular segment AB.

 

 Oct 16, 2020
 #1
avatar+10324 
+1

Minor arc AB in the diagram is 30 degrees and the radius of the circle is 16. Find the area of circular segment AB.

 

Hello Guest!

 

\(A=\frac{30}{360}\cdot \pi\cdot r^2-\frac{1}{2}\cdot r\cdot h\)

 

\(\color{BrickRed}r=16\\ h=r\cdot sin\ {\color{BrickRed}30°}=16\cdot 0.5\\ \color{blue}h=8\)

 

\(A=\frac{1}{12}\cdot \pi\cdot 16^2-\frac{1}{2}\cdot 16\cdot 8\)

\(A=3.021\)

laugh  !

 
 Oct 16, 2020
edited by asinus  Oct 16, 2020
 #2
avatar+27695 
+1

Area of entire sector - triangle = shaded area

30 / 360 * pi r^2  - 1/2 ab sin30

30/360 * pi * 162 - 1/2 (16)(16) sin30 = 3.0206  units2

 
 Oct 16, 2020

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