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2. 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.

2. 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.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 8740 Points
4 months ago
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 So, 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 Or, πR2 = 100πcm2 R2 = 100cm2 So, R = 10cm

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