Given, the diameter of two circles are 3 : 4

Let the diameter of the first circle = 3x

So, radius of the first circle = 3x/2

and diameter of the second circle = 4x

So, radius of the second circle = 4x/2 = 2x

Now, according to question,

     π(3x/2)² + π(2x)² = π(30/2)²

=> (3x/2)² + (2x)² = (15)²

=> 9x² /4 + 4x² = 225

=> (9x² + 16x² )/4 = 225

=> 25x² /4 = 225

=> x² /4 = 225/25

=> x² /4 = 9

=> x² = 9*4

=> x² = 36

=> x = √36

=> x = ±6

=> x = 6  {since x ≠ -6}

So, the the diameter of the first circle = 3x = 3*6 = 18 cm

and the diameter of the second circle = 4x = 4*6 = 24 cm