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.
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.
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Answer:Area of first circle = πr2
= π82 = 64π sq cm
Area of second circle = π62 = 36π sq cm
As per question; area of the largest circle = 64π + 36π
= 100π sq cm
Or, πr2 = 100π
Or, r2 = 100
Or, r = 10 cm
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Here, `r_1 = 8cm and r_2 = 6cm`
So, `A_1 = pir_1^2 and A_2 = pir_2^2`
`A_1 = 64pi and A_2 = 36pi`
Now. let radius of the circle having area equal to the sum of the areas of these two circles is `r_3`. Then,
`pir_3^2 = 64pi+36pi = 100pi`
`=>r_3^2 = 100=>r_3 = 10`
So, radius of the third circle will be `10cm`.
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