The formula to find the area $A$ of a circle is:

$A = \pi r^2$

where $r$ is the radius of the circle. The radius is half of the diameter. Given that the diameter is 15 cm, the radius $r$ is:

$r = \frac{15}{2} = 7.5 \, \text{cm}$

Now, substitute $r$ into the formula for the area:

$A = \pi (7.5)^2 = \pi \times 56.25 \, \text{cm}^2$

Approximating $\pi$ as 3.1416:

$A \approx 3.1416 \times 56.25 \approx 176.71 \, \text{cm}^2$

So, the area of the circle is approximately 176.71 cm².

Would you like more details or have any questions?

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Here are 5 related questions to expand your understanding:

1. What is the circumference of a circle with a diameter of 15 cm?
2. How would the area change if the diameter doubled?
3. What is the area of a circle with a radius of 10 cm?
4. How is the formula for the area of a circle derived?
5. What is the area of a sector with a 90° angle from the same circle?

Tip: Always remember that the radius is half the diameter when working with circle formulas!