Question

a circle with center o and angle AOB =90 degree . if the radius of the circle is 40 CM. calculate the area of the shaded region of the circle.

Answer 1

area of sector =1/4×22÷7×40×40=1257.1
area of triangle=1÷2×40×40=800
1257.1-8000
ans= 457.1

Answer 2

Answer:

The area of shaded region is 456 cm²

Step-by-step explanation:

A circle with center O and ∠AOB =90°. If radius of the circle is 40 cm.

Area of triangle AOB,  $A_T=\dfrac{1}{2}\times OA\times OB$

                                    $A_T=\dfrac{1}{2}\times 40\times 40$

                                    $A_T=800\text{ cm}^2$

Area of sector AOB, $A_S=\dfrac{\theta}{360^\circ}\times \pi r^2$

                                  $A_S=\dfrac{90}{360}\times \pi\times 40^2$

                                  $A_S=400\pi\text{ cm}^2$

Area of shaded region = Area of sector - Area of triangle

                                   $=A_S-A_T$

                                   $=400\pi-800$

                                   $=400(\pi-2)\text{ cm}^2\approx 456\ cm^2$

Hence, The area of shaded region is 456 cm²