1. **State the problem:** We need to find the area of a circular cupcake cup with radius $18$ millimeters. 2. **Formula:** The area $A$ of a circle is given by the formula: $$A = \pi r^2$$ where $r$ is the radius. 3. **Substitute the radius:** $$A = \pi \times 18^2$$ 4. **Calculate the square of the radius:** $$18^2 = 324$$ 5. **Calculate the area:** $$A = \pi \times 324$$ 6. **Use the approximate value of $\pi \approx 3.1416$:** $$A \approx 3.1416 \times 324 = 1017.8764$$ 7. **Round to the nearest hundredth:** $$A \approx 1017.88$$ square millimeters. **Final answer:** The area of the cupcake cup is approximately $1017.88$ square millimeters.