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23/06/2021 10:50 am
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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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23/06/2021 10:52 am
Radius of 1st circle = 8 cm (given)
∴ Area of 1st circle = π(8)2 = 64π
Radius of 2nd circle = 6 cm (given)
∴ Area of 2nd circle = π(6)2 = 36π
The sum of 1st and 2nd circle will be = 64π+36π
= 100π
Now, assume that the radius of 3rd circle = R
∴ Area of the circle 3rd circle = πR2
It is given that the area of the circle 3rd circle = Area of 1st circle + Area of 2nd circle
πR2 = 100π cm2
R2 = 100 cm2
R = 10cm