Question

Find the area of the major segment APB, in Fig 5, of a circle of radius 35 cm and ∠AOB = 90°. (Use $\pi = \frac{22}{7}$)

Answer 1

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Answer 2

Answer:  The required area is 3500 cm²

Step-by-step explanation:

Given: angle of minor sector = 90°

Therefore angle of major sector = 360°-90°= 270°

Radius of circle = 35 cm

Area of major segment APB= area of major sector + area of Δ AOB

$Area= \pi r^2\dfrac{\theta}{360} + \dfrac{1}{2} \times base\times height\\\\= \dfrac{22}{7} \times 35 \times 35 \times \dfrac{270}{360} + \dfrac{1}{2} \times 35\times 35\\\\= 35\times 35( \dfrac{22}{7} \times \dfrac{3}{4} +\dfrac{1}{2} )\\\\=1225( \dfrac{33}{14} +\dfrac{1}{2})\\\\=1225\times (\dfrac{33+7}{14}  )\\\\= 1225\times \dfrac{40}{14} \\\\= 3500cm^2$

Hence, the required area is 3500 cm²