Question

find the radius of a circle having area equal to the sum of the areas of two circles with radius 20cm and 15cm respectively

Answer 1

sum of areas of 2 circles - 
r1 = 20 cm
r2 = 15 cm
 
∴sum of areas = (π x 20 x 20) + (π x 15 x 15)
                        = 400π + 225π
                        = 625π

∴ area of other circle = 625π cm²

∴ πr² = 625π 
∴ r² = 625
∴r = √625
∴r = 25 cm