A circular disc of radius 6cm is divided into 3 sectors with central angles 120 degree , 150 degree and 90 degree . What part of the whole area is the area of the sector with central angle 120 degree ? Also find the ratio of the areas ofg the 3 sectors .

Dear Student,

Please find below the solution to the asked query:

Given :  radius of a circle  = 6  cm ,

We know area of circle  = $\mathrm{\pi }$r²  , Here r  =  Radius of circle , So

Area of given circle  = $\mathrm{\pi }$ (6² ) = 36 $\mathrm{\pi }$ cm²

And

We know area of sector of circle  = $\frac{\mathrm{Center} \mathrm{angle}}{360°}\times$$\mathrm{\pi }$r²  , So

Area of sector of circle with center angle 120$°$  = $\frac{120°}{360°}\times \mathrm{\pi }\times 6^2 = \frac{1}{3}\times \mathrm{\pi }\times 36$  = 12 $\mathrm{\pi }$ cm²

Therefore,

Area of whole circle  =  3 ( Area of sector of circle with center angle 120$°$  )                                  ( Ans )

And

Area of sector of circle with center angle 150$°$  = $\frac{150°}{360°}\times \mathrm{\pi }\times 6^2 = \frac{5}{12}\times \mathrm{\pi }\times 36 = 5 \times 3 \times \mathrm{\pi }$  = 15 $\mathrm{\pi }$ cm²
And

Area of sector of circle with center angle 90$°$  = $\frac{90°}{360°}\times \mathrm{\pi }\times 6^2 = \frac{1}{4}\times \mathrm{\pi }\times 36$  = 9 $\mathrm{\pi }$ cm²
Then,

Area of sector of circle with center angle 120$°$  : Area of sector of circle with center angle 150$°$  : Area of sector of circle with center angle 90$°$   = 12$\mathrm{\pi }$ : 15 $\mathrm{\pi }$  : 9 $\mathrm{\pi }$

Therefore,

Area of sector of circle with center angle 120$°$  : Area of sector of circle with center angle 150$°$  : Area of sector of circle with center angle 90$°$   = 4 : 5  : 3                                                            ( Ans )


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