chord of a circle of radius 20 cm subtends an angle of 90 degree at the centre find the area of the corresponding arc of sector
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chord of a circle of radius 20 cm subtends an angle of 90 degree at the centre find the area of the corresponding arc of sector
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Given:
To find:
Solution:
To find the area of the sector, we use the formula:
⟶ Area of sector = θπr^2/360
where,
On applying area of sector formula, we get:
⟶ Area of sector = (90×22/7×20^2)/360
⟶ Area of sector = (90×22/7×400)/360
⟶ Area of sector = (22/7×36000)/360
⟶ Area of sector = (792000/7)/360
⟶ Area of sector = 113142.857/360
⟶ Area of sector = 314.28cm^2
Final Answer:
Step-by-step explanation:
Area of circle=πr²
=πr²
=314/100*20*20
=1256 cm²
area of minor segment =theta/360*πr² -1/2*r²sin theta
=90*314*20*20/360*100 -1/2*20²(1)
=314-200
114cm²
area of major segment=area of circle -area of minor segment
=1256-114
=1142 cm²