Question

Find the area of the major segment APB in adjoining figure , of a circle of radius 35cm and angle AOB =90°.

Answer 1

As we know it's an right angled triangle Using Pythagoras theorem, AB^2=AO^2+BO^2 AO=BO=35 AO^2+BO^2=35^2+35^2 AB^2=1225+1225 AB=√2450 AB=√2×5×5×7×7 AB=5×7×√2 AB=35√2cm

Answer 2

Answer:

3500 cm²

Step-by-step explanation:

Hi,

Given radius of the circle R = 35 cm

Area of major segment APB = Area of major sector OAPBO

+ Area of the Δ AOB

Area of major sector OAPBO

Since the sector makes an angle of 270° at center,

Area of sector = 1/2*R²* (3π/2)

= 3/4*π*R²

= 3/4*22/7*35*35 cm²

= 2887.5 cm²

Area of ΔAOB = 1/2*OA*OB sin90

= R²/2

= 35*35/2

= 612.5 cm²

Area of major sector = 2887.5 cm² + 612.5 cm²

= 3500 cm².

Hence, Ara of major segment = 3500 cm².

Hope, it helps !