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Question
The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.
Solution
Radius (r1) of 1st circle = 8 cm
Radius (r2) of 2nd circle = 6 cm
Let the radius of 3rd circle be r.
Area of 1st circle = `Pir_1^2 = pi(8)^2 = 64pi`
Area of 2nd circle = `Pir_2^2 = pi(6)^2 = 36pi`
Given that,
Area of 3rd circle = Area of 1st circle + Area of 2nd circle
`pir^2 = pir_1^2 + pir_2^2`
`pir^2 =64pi + 36pi`
`pir^2 = 100pi`
r2 = 100
r = ±10
However, the radius cannot be negative. Therefore, the radius of the circle having area equal to the sum of the areas of the two circles is 10 cm.
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