Question

the central angle of a sector of circle of area 9π cm sq is 60° find the perimeter of sector​

Answer 1

Answer:

Perimeter of sector = ( 6 + π )√6 cm

Step-by-step explanation:

Area of sector = 9π

Angle of Sector = 60°

Area of sector = πr² ( angle of sector/360)

9π  = πr² (60/360)

r² = 54

r = 3√6

So, Radius of circle = 3√6 cm

Now, Arc length of the sector = 2πr (angle of sector/360)

                                              =  2π × 3√6 × (1/6)

                                              =    π√6

So, Perimeter od sector = 2r + Arc length of sector

                                        = 2 × 3√6 +  π√6

                                        =  ( 6 + π ) √6 cm