Question

The area of segment of a circle whose radius is 14 cm and the angle at the centre is 90°

Answer 1

Step-by-step explanation:

Given radius(r)=14cm

⇒ Area of sector OABO=360oθπr2

∴ Area of sector OABO=360o90o×722×(14)2=154cm2

⇒ Area of right angled △OAB=21×14×14=98cm2

∴ Area of the minor segment of the circle = Area of sector OABO - Area of righta angled △ABO

∴ Area of the minor segment of the circle =(154−98)cm2=56cm2

⇒ Area of circle =πr2=722×14×14=616cm2

⇒ Area of the major segment of the circle = Area of circle - Area of minor segment.

∴ Area of the major segment of the circle =(616−56)cm2=560cm2

Answer 2

Given radius(r)=14cm

⇒ Area of sector OABO=360oθπr2

∴ Area of sector OABO=360o90o×722×(14)2=154cm2

⇒ Area of right angled △OAB=21×14×14=98cm2

∴ Area of the minor segment of the circle = Area of sector OABO - Area of righta angled △ABO

∴ Area of the minor segment of the circle =(154−98)cm2=56cm2

⇒ Area of circle =πr2=722×14×14=616cm2

⇒ Area of the major segment of the circle = Area of circle - Area of minor segment.

∴ Area of the major segment of the circle =(616−56)cm2=560cm2

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