The central angles of two sectors 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?

Radius of one sector = r1 = 7 cm


Radius of second sector = r2 = 21 cm


Central angle of one sector = 120°


Central angle of second sector = 40°


Central angle of one sector (in radians) = θ1 = (120π/180)


Central angle of second sector (in radians) = θ2 = (40π/180)


Area of first sector =



= =


154/3 = 51.33 cm2


Area of second sector =


=



= 154 cm2


Let the lengths of the corresponding arc be l1 and l2.


Now, arc length of first sector = Radius × Central Angle (in radians)


= = 44/3 cm


Now, arc length of second sector = Radius × Central Angle (in radians)


= = 44/3 cm


Hence, we observe that arc lengths of two sectors of two different circles may be equal but their area need not be equal.


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