The radii of two circles are 8cm and 6cm respectively. Find the radius of the circle having an area equal to the sum of the areas of the two circles.
1 Answer
Solution:
Given,
The radius of the 1st circle = 8 cm
∴ Area of the 1st circle = 𝜋 (8)2 = 64𝜋
The radius of the 2nd circle = 6 cm
∴ Area of the 2nd circle = 𝜋 (6)2 = 36𝜋
So,
The sum of the Area of two circles = 64𝜋 + 36𝜋 = 100𝜋
Now, assume that the radius of the 3rd circle = R
∴ The Area of the 3rd circle = 𝜋R2
It is given that the area of the 3rd circle = Area of 1st circle + Area of 2nd circle
Or, 𝜋R2 = 100𝜋 cm2
R2 = 100 cm2
So, R = 10 cm
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