Question

prove that area of the sector of angle theta is equal to theta upon 360 into Pi R Square

Answer 1

Area of circle = πr^2
Area of 360° sector = πr^2
Area of ∅° sector = πr^2/360 ×∅

Or it can be written as

∅/360 × πr^2

Answer 2

Answer:

Step-by-step explanation:

So if the central angle made by the sector is θ degrees then the area should be (θ/360)(πr^2)

In radian measure the length l of the arc is given by l = rθ where θ is measured in radians (π radians = 180 degrees)

In radian measure, the area A of sector of a circle is given by A = 1/2 r^2 θ = 1/2 r rθ = 1/2 rl.

Hence the area of a sector is (θ/360)(πr^2) in degree measure and is = 1/2 rl in radian measure.