22. The Fig. 17.24 shows a circle with centre at O and ZAOB = 90°. If the radius of the circle is 40cm calculate the area of shaded portion of the circle
Answers
Answer:
-by-step explanation:
A circle with center O and ∠AOB =90°. If radius of the circle is 40 cm.
Area of triangle AOB, A_T=\dfrac{1}{2}\times OA\times OBA
T
=
2
1
×OA×OB
A_T=\dfrac{1}{2}\times 40\times 40A
T
=
2
1
×40×40
A_T=800\text{ cm}^2A
T
=800 cm
2
Area of sector AOB, A_S=\dfrac{\theta}{360^\circ}\times \pi r^2A
S
=
360
∘
θ
×πr
2
A_S=\dfrac{90}{360}\times \pi\times 40^2A
S
=
360
90
×π×40
2
A_S=400\pi\text{ cm}^2A
S
=400π cm
2
Area of shaded region = Area of sector - Area of triangle
=A_S-A_T=A
S
−A
T
=400\pi-800=400π−800
=400(\pi-2)\text{ cm}^2\approx 456\ cm^2=400(π−2) cm
2
≈456 cm
2
Hence, The area of shaded region is 456 cm²
Answer:
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