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Areas related to Circles ncert solutions Chapter 12 Exercise 12.2 Question 4

Areas related to Circles ncert solutions Chapter 12 Exercise 12.2 Question 4


 

4.     A chord of a circle of radius 10 cm subtends a right angle at the center. Find the area of the corresponding: (i) minor segment   (ii) major segment. (Use \pi=3.14)

 

Solution:

CBSE ncert solutions areas related to circles

AO = OB = 10 cm (Radii of circle)

 

Area of sector of circle = \pi.r^2 \times \frac{\theta}{360^\circ}

Angle of sector for major sector is equal to 360-90 =270^\circ

 

\Rightarrow Area of major sector =Area shaded in light blue= 3.14 \times 10 \times 10 \times \frac{270^\circ}{360^\circ}=235.5 cm^2

 

Area of minor segment=Area shaded in green

=Area of circle - area of major sector-Area of triangle \triangle AOB

 

\Rightarrow Area of minor segment=\pi.r^2-235.5-\frac{1}{2}.OA.OB

\Rightarrow Area of minor segment=3.14 \times 10 \times 10-235.5-\frac{1}{2} \times 10 \times 10

=314-235.5-50=28.5 cm^2


 


Posted in : Areas related to Circles, Circles, NCERT Solutions


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2 thoughts on “Areas related to Circles ncert solutions Chapter 12 Exercise 12.2 Question 4


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