A chord with a length of #5 # runs from #pi/8 # to #pi/2 # radians on a circle. What is the area of the circle?

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Answer 1 · 2017-08-03T11:29:15

The area of the circle is 63.62 # sq.unit.

Formula for chord length is # C_l = 2*r * sin (c/2) # , where #c# is the

angle subtended at the centre by the chord and #r# is the radius of

the circle. Here #C_l=5 , c= (pi/2 -pi/8) = 180/2 - 180/8 #

#=90-22.5 = 67.5^0 ; r = C_l/(2*sin(c/2)) = 5/(2*sin 33.75) # or

# r = 5/1.11 ~~ 4.5# .

The area of the circle is #A=pi*r^2 = pi* 4.5^2 ~~ 63.62 # sq.unit

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