Circular Measure? I checked the marking scheme but still dont understand Question in the details below..

enter image source here

1 Answer
CW
Aug 20, 2017

see explanation.

Explanation:

enter image source here
Let #r# be the radius of the circle.
(1) Minor arc length #AB=rtheta#, (#theta# in radians)
Major arc length #AB=r(2pi-theta)#
Perimeter of #R1=r+r+rtheta=2r+rtheta=r(2+theta)#
#=> cancelr(2+theta)=cancelr(2pi-theta)#
#=> 2+theta=2pi-theta#
#=> 2theta=2pi-2#
#=> theta=pi-1# (proved)

(2) Area of #R1=1/2r^2theta#, (#theta# in radians)
#=> 1/2 r^2theta=30#
#=> r^2=(2*30)/theta=60/(pi-1) " cm"^2#

Area of #R2=1/2r^2(2pi-theta)#
#= 1/2*(60)/(pi-1)*(2pi-(pi-1))#
#=1/2*60/(pi-1)*(pi+1)#
#= 30xx(pi+1)/(pi-1)#
#~~58.0 " cm"^2#, (3 significant figures)

Related questions
Impact of this question
1015 views around the world
You can reuse this answer
Creative Commons License