1. The problem states that the diameter $d$ of a circle is 8 centimeters, and we need to find the area of the circle rounded to the nearest hundredth. 2. Recall the formula for the area $A$ of a circle: $$A = \pi r^2$$ where $r$ is the radius of the circle. 3. The radius $r$ is half the diameter, so $$r = \frac{d}{2} = \frac{8}{2} = 4 \text{ cm}.$$ 4. Substitute $r = 4$ cm into the area formula: $$A = \pi (4)^2 = 16\pi.$$ 5. Using the approximation $\pi \approx 3.14159$, calculate the area: $$A \approx 16 \times 3.14159 = 50.26544.$$ 6. Round the result to the nearest hundredth: $$A \approx 50.27 \text{ square centimeters}.$$ Therefore, the area of the circle is approximately 50.27 square centimeters.