Question

A chord of a circle of radius 20 cm subtends an angle of 90° at the centre. Find the area of the corresponding major segment of the circle.

Answer 1

radius =20cm
theta= 90°
area of minor segment = πr²theta/360-1/2r²sintheta
= 22/7×20×20×90/360-1/2×20×20×sin90°. [sin90°=1]
Solve this u will the area of minor segment..
Therefore,
major segment = πr²-(@rea of minor segment)

Answer 2

Answer:

The area of major segment of the circle is 1142.47 cm².

Step-by-step explanation:

The radius of the circle is 20 cm. The subtends angle is 90 degree at the center.

The formula to find the area of minor segment is

$A_1=\pi r^2\times \frac{\theta}{360}-\frac{1}{2}\times r^2\sin \theta$

$A_1=\pi (20)^2\times \frac{90}{360}-\frac{1}{2}\times (20)^2\sin (90)$

$A_1=\pi (20)^2\times \frac{1}{4}-\frac{1}{2}\times (20)^2(1)$

$A_1=114.16$

The area of circle is

$A_2=\pi r^2$

$A_2=\pi (20)^2$

$A_2=1256.63$

The area of major segment of the circle is

$A=A_2-A_1=1256.63-114.16=1142.47$

Therefore the area of major segment of the circle is 1142.47 cm².