Final answer:
To find the room available for spreading frosting on the top of the cake, calculate the area of the top surface of the cake.
Step-by-step explanation:
To find the room available for spreading frosting on the top of the cake, we need to calculate the area of the top surface of the cake.
The cake has a diameter of 18 centimeters, so the radius (half the diameter) is 9 centimeters.
The area of a circle is calculated using the formula A = πr^2, where π is a mathematical constant approximately equal to 3.14159.
Therefore, the area of the cake's top surface is A = 3.14159 * 9^2 = 254.469 square centimeters.