A circle has a chord that goes from #pi/4 # to #(5 pi) / 8 # radians on the circle. If the area of the circle is #90 pi #, what is the length of the chord?

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A circle has a chord that goes from #pi/4 # to #(5 pi) / 8 # radians on the circle. If the area of the circle is #90 pi #, what is the length of the chord?

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Answer 1 · 2016-08-19T08:06:53

#=11.176#

Explanation:

A chord that goes from #(pi)/4#to #(5pi)/8#
so it travels the distance #(5pi)/8-(pi)/4=(3pi)/8#;
or
#(3pi)/8-:2pi=3/16# of the Circumference of the Circle
Area of the Circle#=pir^2=90pi#
or
#r^2=90#
or
#r=sqrt90#
or
#r=9.48#
Circumference of the circle#=2pir=2(pi)(9.48)=59.6#
Therefore Length of the chord#=59.6times3/16=11.176#

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A circle has a chord that goes from #pi/4 # to #(5 pi) / 8 # radians on the circle. If the area of the circle is #90 pi #, what is the length of the chord?

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