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

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Sum

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

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#### Solution

Given that, radius of the circle (r) = 21 cm and central angle of the sector AOBA (θ) = 120°

So, area of the circle = pir^2 = 22/7 xx (21)^2 = 22/7 xx 21 xx 21

= 22 xx 3 xx 21

= 1386 cm2

Now, area of the minor AOBA with central angle 120°

= (pir^2)/360^circ  xx theta = 22/7 xx (21 xx 21)/360^circ xx 120

= (22 xx 3 xx 21)/3

= 22 xx 21

= 462 cm2

∴ Area of the amjor sector ABOA = Area of the circle – Area of the sector AOBA

=1386 – 462

= 924 cm2

∴ Difference of the areas of a sector AOBA and its corresponding major sector ABOA

= |Area of major sector ABOA – Area of minor sector AOBA|

= |924 – 462|

= 462 cm2

Hence, the required difference of two sectors is 462 cm2

Concept: Areas of Sector and Segment of a Circle
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 11 Area Related To Circles
Exercise 11.4 | Q 20 | Page 135
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