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  • Find the difference of the areas of a sector of angle 120° and its corresponding major sector of a circle of radius 21 cm.

Find the difference of the areas of a sector of angle 120° and its corresponding major sector of a circle of radius 21 cm.

Answers (1)

Answer [462 cm2]

Solution

            

Radius = 21 cm

Angle = 120°

Area of circle = \pi r^{2}

  \\=\frac{22}{7}\times 21\times 21\\ =1386 cm^{2}

Area of minor sector with angle 120° OABO =\frac{\pi r^{2} \theta}{360}                                   \left [ \theta =120^{\circ} \right ]                                                                                   

                                                              \\=\frac{22}{7}\times \frac{21\times 21}{360}\times120\\ =462cm^{2}

Area of major sector AOBA= Area of circle – area of minor sector

                                           = 1386-462=924cm2

Required area =924-462=462cm2

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