Question

the perimeter of the sector of the circle of area 64 Pi square cm is the 56 cm find the area of the sector​

Answer 1

hlo mate

Area of circle = 64 pi

=> pi r^2 = 64 pi

=> r^2 = 64

=> r = 8

Radius of circle = 8 cm

Now,

Perimeter of sector = 56

=> 2 × Radius + Length of arc = 56

=> 2 × 8 + Length of arc = 56

=> Length of arc = 56 - 16

=> Length of arc = 40 cm

=> 2 pi R ( theta / 360) = 40

=> 2 × pi × 8 × ( theta) / 360 = 40

=> Theta = 40 × 360 / 16 pi

=> Theta = 5 × 180 / pi

Now,

Area of sector = pi r^2 ( theta / 360)

= pi × 8 × 8 × ( 5 × 180 / pi ) / 360

= 64 pi ( 900/ pi) / 360

= 64 pi × 900 / 360 × pi

= 64 × 900 /360

= 64 × 10 / 4

= 16 × 10

= 160 cm^2

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