Math, asked by golukumar89698p2w4e7, 10 months ago

find area of green circle​

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Answers

Answered by bhagyashreechowdhury
0

Given:

Attached figure in the question

To find:

The area of the green circle

Formula to be used:

  • Pythagoras Theorem: Hypotenuse² = Perpendicular² + Base²

Solution:

Let’s take some assumptions just as shown in the figure attached below:

AO’ = BO’ = radius of the smaller circle = “r”

AO = OC = radius of the larger circle

DE = 10 cm

BC = 18 cm

GF = 10 cm

Construction to be done: Join O’ and E where O’E = radius of the smaller circle = “r”

So, we have  

The diameter of the larger circle, AC = r + r + 18 = (2r + 18) cm

∴ The radius of the larger circle, AO = CO = diameter/2 = ½ * (2r+18) = (r + 9) cm

Also, we get the distance between the centers of the circle O and O’ as (r+9) – r = 9 cm

Since OG & OD is also the radius of the larger circle

OE = OD – DE = (r + 9) – 10 = (r - 1) cm

Consider triangle OO’E and on applying the Pythagoras theorem we get

O’E² = OE² + OO’²

⇒ r² = (r - 1)² + 9²

⇒ r² = r² – 2r + 1 + 81

⇒ r² – r² + 2r = 82

⇒ 2r = 82

r = 41 cmradius of the smaller circle AO’ or BO’

∴ The radius of the larger circle = AO = CO = r + 9 = 41 + 9 = 50 cm

Now, to find the area of the green circle we will subtract the area of the smaller circle from the area of the larger circle.

Therefore,

The area of the green circle is given by,

= [Area of the larger circle] – [Area of the smaller circle]

= [π(r+9)²] – [πr²]

Substituting the value of r = 41 cm and r + 9 = 50 cm

= [π (50)²] – [π (41)²]

= π [(50)² – (41)²]

= π [2500 – 1681]  

= 819π cm² or 2574 cm² (taking π = 22/7)

Thus, the area green circle is 819π cm² or 2574 cm².

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Also View:

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Find the area of shaded region in figure, where a circle of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm

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Answered by anjanaramesh07
0

Answer:

find the green area please solve

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