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.

Answer 1

Radius (r₁) of 1^st circle = 8 cm

Radius (r₂) of 2^nd circle = 6 cm

Let the radius of 3^rd circle be r.

Area of 1^st circle  = `Pir_1^2 = pi(8)^2 = 64pi`

Area of 2^nd circle = `Pir_2^2 = pi(6)^2 = 36pi`

Given that,

Area of 3^rd circle = Area of 1^st circle + Area of 2^nd 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.