The area $A$ of a circle is given by the formula:

$A = \pi r^2$

Where $r$ is the radius of the circle. The radius is half the diameter, so:

$r = \frac{8}{2} = 4 \text{ cm}$

Now substitute $r = 4$ cm into the formula:

$A = \pi (4)^2 = \pi \times 16$

Thus, the area is:

$A = 16\pi \text{ cm}^2$

Approximating $\pi$ as 3.1416:

$A \approx 16 \times 3.1416 = 50.27 \text{ cm}^2$

So, the area of the circle is approximately 50.27 cm².

Would you like more details or have any questions?

Here are 5 related questions for practice:

1. What is the circumference of a circle with a diameter of 8 cm?
2. How would the area change if the diameter were doubled?
3. If the area of a circle is 50.27 cm², what is its radius?
4. What is the area of a circle with a radius of 5 cm?
5. How does the area of a circle relate to the square of its radius?

Tip: Remember that the radius is always half the diameter when calculating properties of a circle!