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