38. In the gven figure, AB and CD are two diameters of a
circle (with centre O) perpendicular to each other and OD
is the diameter of the smaller circle. If OA = 7 cm, find the
area of the shaded region.
Answers
Answer:
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Given :--
- OA = radius of Big circle = 7cm.
- AB = CD = diameters.
To Find :-
- Shaded Total Area ?
Solution :---
From image we can see that, DO is also radius of big circle and that is also 7cm.
Now,
→ DO also = Diameter of small circle inside it .
So, we can say that, Radius of small circle is = (7/2)cm .
So, Shaded Area of smaller circle = πr² = (22/7) * (7/2)² = 38.5cm.²
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Now, lets see other shaded Area,
That is equal to = Semicircle - Area of ∆BCA
We have semicircle with radius = 7cm .
and,
∆ with Base as Diameter of circle and Height as radius of circle.
So, we can say that,
→ shaded area = (πr²)/2 - 1/2 (2r) * r [ as Area of ∆ = 1/2 * Base * Height ]
Putting values now we get,
→ Shaded Area = 1/2* [(22/7) * (7)² ] - (7)²
→ shaded area = 77 - 49 = 28cm² .
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Hence, Total shaded Area will be = 38.5 + 28 = 66.5cm² ..