Question

The central angle of 2 sectors of radii 7cm and 21cm are respectively 120degree and 40degree find the area of the two sectors as well as the length of the irresponsible arc

Answer 1

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We observe that both the sectors of 2 different circles have different areas but having the same arc length.

Answer 2

Area =  154/3  cm²  Length of arc 44/3  cm & Area =  154 cm²  Length of arc 44/3  cm

Step-by-step explanation:

The central angle of 2 sectors of radii 7cm and 21cm are respectively 120degree and 40degree

Area of sector circle = (segment Angle /360) * π r²

Length of arc = (segment Angle /360) * 2π r

r = 7 cm

Angle = 120°

π = 22/7

Area = (120/360) (22/7) * 7²   = 154/3  cm²

Length of arc (120/360)(2 * (22/7) * 7) = 44/3  cm

r = 21 cm

Angle = 40°

π = 22/7

Area = (40/360) (22/7) * 21²   = 154  cm²

Length of arc (40/360)(2 * (22/7) * 21) = 44/3  cm

Length of arc is same in both cases

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