The sum of the areas of two circle $A$ and $B$ is equal to the area of a third circle $C$, whose diameter is $30$ cm. If the diameter of circle $A$ is $18$ cm, then the radius of circle B is

Using the area of a circle, pi times radius squared, the sum of the areas of circles A and B equals the area of circle C. This gives pi times 9 squared plus pi times the radius of B squared equals pi times 15 squared. Dividing by pi yields 81 plus the radius of B squared equals 225, so the radius of B squared equals 144. Taking the square root gives the radius of circle B as 12 centimeters.

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