find area of green circle
Answers
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 cm ← radius 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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Answer:
find the green area please solve