In fig .12.27 , AB and CD are the two diameter of a circle ( with centre O ) prepandicular to each other and OD is the diameter of the smaller circle . If OA = 7cm , find the area of the shaded region ?
Answers
Answer:
66.5 cm²
Step-by-step explanation:
Given, Radius of larger circle R = OA = OB = OD = 7 cm.
Then, radius of smaller circle (r) = 3.5 cm.
From ΔBCA:
Base = OC = 7 cm.
Height = AB = 14 cm.
Area = (1/2) * OC * AB
= (1/2) * 7 * 14
= 49 cm²
Now,
(i) Area of larger circle = πR²
= (22/7) * (7)²
= 154 cm²
(ii) Area of larger semicircle = πR²/2
= 154/2
= 77 cm²
(iii) Area of smaller circle = πr²
= (22/7) * (3.5)²
= 38.5 cm²
∴ Area of shaded region :
= Area of larger semicircle - Area of ΔBCA + Area of smaller semicircle
= 77 - 49 + 38.5
= 66.5 cm²
Therefore, Area of the shaded region = 66.5 cm²
Hope it helps!
Area of a circle = pie r ²
= 154 cm²
Area of shaded region = r² (pie theta/ 360- sin theta / 2)
= 14 cm²