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The central angles of two sectors of circles of radii 7 cm and 21 cm are
respectively 120° and 40°. Find the areas of the two sectors as well as the
lengths of the corresponding arcs. What do you observe?

CASE 1:radius of the circle, r1 = 7 cmcentral angle, θ1 = 120°area of sector of circle = θ1360°×πr12 = 120°360°×227×7×7 = 1543 cm2length of the arc =θ1360°×2πr1  =   120°360°×2×227×7 = 443 cmCASE 2:radius of the circle, r2 = 21 cmcentral angle, θ2 = 40°area of sector of circle = θ2360°×πr12 = 40°360°×227×21×21 = 154 cm2length of the arc =θ2360°×2πr2 =   40°360°×2×227×21 = 443 cm

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

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