A chord with a length of #14 # runs from #pi/3 # to #pi/2 # radians on a circle. What is the area of the circle?

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Answer 1 · 2016-08-23T11:00:46

#=2246#

A chord travels #pi/2-pi/3=pi/6# radians of the Circle

In other words chord travels #pi/6-:2pi=1/12 th# of Circumference

Circumference#=2pir# where #r=radius#

Therefore we can write

Length of the Chord #=14=(2pir)/12#

or

#2pir=14times12#

or

#r=168/(2pi)#

or

#r=26.74#

Area of the Circle#=pir^2#

#=pi(26.74)^2#

#=2246#