Answer:
Option (3)
Step-by-step explanation:
From the figure attached,
Area of the shaded region = Area of circle - (Area of the ΔOAB + Area of ΔOED)
Area of the circle = πr²
= π(5)²
= 25π cm²
Area of ΔOAB = 2(Area of ΔOCB)
AB = 6 cm
OC = 5 - 1 = 4 cm
By applying Pythagoras theorem in ΔOCB,
OB² = OC² + BC²
5² = 4² + BC²
BC² = 25 - 16
BC = √9 = 3 cm
Area of ΔOCB = [tex]\frac{1}{2}(OC)(BC)[/tex]
= [tex]\frac{1}{2}(4)(3)[/tex]
= 6 cm²
Area of ΔAOB = 2(6) = 12 cm²
Area of ΔAOB = Area of ΔDOE = 12 cm²
Area of shaded region = 25π - (12 + 12)
= (25π - 24) cm²
Therefore, Option (3) will be the answer.
