Question

in the figure given below a AOBC is a quadrant of a circle of radius 10 m .calculate the area of the shaded portion. take Pi = 3.14 and give your answer correct to two significant figures

Answer 1

Answer:

28.5 cm²

Step-by-step explanation:

Given: r = 10cm, π = 3.14

ar(shaded region) = ar(quadrant) - ar(ΔAOB)

= (πr²)/4 - (b*h)/2

= (3.14*10*10)/4 - (10*10)/2

= 157/2 - 50

= 57/2

= 28.5 cm²

Answer 2

Area of the shaded portion is 28.5 $(m^{2})$.

Step-by-step explanation:

1. Here radius of quadrant circle (R) = 10 m

2.Area of quadrant circle(AOBC) = $\frac{1}{4}\times \pi \times R^{2}$  ...1)

3. Area of right angle triangle (AOB) =$\frac{1}{2}\times OA \times OB$=$\frac{1}{2}\times R \times R$

  So

  Area of right angle triangle (AOB) =$\frac{1}{2}\times R \times R=\frac{1}{2}\times R^{2}$   ...2)

4. Area of shaded portion = Area of quadrant circle(AOBC) - Area of right angle triangle (AOB)      ...3)

5.   So from equation 1) and equation 2), equation 3) can be written as

  Area of shaded portion=$\frac{1}{4}\times \pi \times R^{2}-\frac{1}{2}\times R^{2}$  

 

 Area of shaded portion=$\frac{1}{2}\times R^{2}\left [ \frac{\pi }{2}-1 \right ]$     ...4)

6. After putting the value in equation 4)

 Area of shaded portion$=\frac{1}{2}\times 10^{2}\left [ \frac{3.14 }{2}-1 \right ]=28.5 m^{2}$