To determine the exact area of a circle with a diameter of 10 cm, we follow these steps:
1. Determine the radius of the circle: - The radius is half of the diameter. Given the diameter is 10 cm, the radius [tex]\( r \)[/tex] is: [tex]\[
r = \frac{\text{diameter}}{2} = \frac{10 \text{ cm}}{2} = 5 \text{ cm}
\][/tex]
2. Use 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] - Substituting the radius into the formula: [tex]\[
A = \pi (5 \text{ cm})^2 = \pi \times 25 \text{ cm}^2 = 25\pi \text{ cm}^2
\][/tex]
Therefore, the exact area of a circle with a diameter of 10 cm is [tex]\( 25\pi \text{ cm}^2 \)[/tex].
