Question

IN 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 =7cm ,, find the area of shaded region......​

Answer 1

Answer:

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 .

Step-by-step explanation: