Show that in a circle of radius r, a sector with a central angle of θ radians has an area 1/2*r^2*θ.?
Show that in a circle of radius r, a sector with a central angle of θ radians has an area 1/2*r^2*θ. Take θ between 0 and 2π. Hint: the area of the circle is π*r^2
anyone know how to do this?
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Hi Julia R,
Notice that an entire circle has an angle of 2π.
The fraction of the sector we are working on with regards to the entire circle is θ/2π
The area of an entire circle is πr^2
The area of the sector which is θ/2π of an entire circle is:
(θ/2π) x (πr^2)
= (θ/2) x r^2
= (1/2) x θ x r^2
= (1/2)r^2 θ
Cheers.