To find the area of a circle with a given diameter, you need to follow these steps:
1. Understand the formula for the area of a circle: The area \(\( A \)\) of a circle is given by the formula:
\(\[
A = \pi r^2
\]\)
where \(\( r \)\) is the radius of the circle.
2. Calculate the radius: The radius \(\( r \)\) is half of the diameter. Given the diameter is 18 cm:
\(\[
r = \frac{d}{2} = \frac{18 \text{ cm}}{2} = 9 \text{ cm}
\]\)
3. Substitute the radius into the area formula:
\(\[
A = \pi r^2 = \pi (9 \text{ cm})^2
\]\)
4. Calculate the square of the radius:
\(\[
9 \text{ cm} \times 9 \text{ cm} = 81 \text{ cm}^2
\]\)
5. Multiply by \(\(\pi\)\):
\(\[
A = \pi \times 81 \text{ cm}^2 = 81\pi \text{ cm}^2
\]\)
Therefore, the area of the circle is \(\( \boxed{81\pi \text{ cm}^2} \)\).
Out of the options given:
- 81π cm²
- 324π cm²
- 18π cm²
- 1296π cm²
The correct answer is \(\( \boxed{81\pi \text{ cm}^2} \)\).
