Saved Bookmarks
| 1. |
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 |
|
Answer» 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 |
|