Question

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​

Answer 1

Given:

• Radius of the circle = 20 cm
• Angle subtended at centre = 90°

To find:

• Area of the sector

Solution:

To find the area of the sector, we use the formula:

⟶ Area of sector = θπr^2/360

where,

• θ = Angle subtended at centre
• r = Radius of the circle

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:

• Area of sector = 314.28cm^2

Answer 2

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