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.

Expert Solution

Radius of 1 circle = 8 cm

Radius of 2 circle = 6 cm

Let the radius of 3 circle = .

Area of 1 circle = π = π(8) = 64π

Area of 2 circle = π = π(6) = 36π

Given that,

Area of 3 circle

st nd rcle = Area of 1 circle + Area of 2 circle

πr = πr 1+ πr2

πr =64π +36π

πr =100π

r =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.

10cm

Nipun Maity answered 2 years ago

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