Question

The diameters of two circles are 32 cm and 24 cm. Find the radius of the circle having its area equal to the sum of the areas of the two given circles.

Answer 1

Let the area of the resulting circle be r.

π x (16)² + π x ( 12 )² = π x r²

             256 π + 144 π = π x r²

                          400π = π x r²

                               r² = 400

                                r = 20 cm

Hence the radius of the resulting circle is 20cm.