the radii of the two circles are 4cm and 3cm. find the radius of the circle whose area is equal to the sum of the areas of the two circles. also find the circumference 

of its circle.

 Let   R=4cm  &   r=3cm        Let the required radius be R'

Area of the circle with radius R = piR²    

                                                         =pi[4]²

                                                        =16pi cm²

Area of the circle with radius r = pir²

                                                        =pi[3]²

                                                       =9pi cm²

Therefore the area of the circlr with radius R' = area of circles with radius r + area of circle with radius R

      piR' ² =16pi + 9pi

pi R' ²= pi [16+9]

{ pi gets cancelled }

R'² =25            R' = 5cm

Therefore the new radius is 5cm

Circumference=2piR'

                           =2 x 22/7 x 5

                           =31.42 cm          [aprox]