To find the area of a circle with a given diameter of 20 cm, we need to follow these steps:
1. Determine the radius:
The radius of a circle is half of its diameter. Given the diameter of the circle is 20 cm, we can find the radius as:
[tex]\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{20 \text{ cm}}{2} = 10 \text{ cm}
\][/tex]
2. Recall the formula for the area of a circle:
The formula for the area [tex]\( A \)[/tex] of a circle is given by:
[tex]\[
A = \pi r^2
\][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
3. Substitute the given values into the formula:
We were given that [tex]\(\pi = 3.14\)[/tex] and from step 1, we found that the radius [tex]\( r \)[/tex] is 10 cm. Substituting these values, we have:
[tex]\[
A = 3.14 \times (10 \text{ cm})^2
\][/tex]
4. Calculate the area:
First, compute [tex]\( (10 \text{ cm})^2 \)[/tex]:
[tex]\[
(10 \text{ cm})^2 = 100 \text{ cm}^2
\][/tex]
Next, multiply by [tex]\(\pi\)[/tex]:
[tex]\[
A = 3.14 \times 100 \text{ cm}^2 = 314 \text{ cm}^2
\][/tex]
Therefore, the area of the circle is [tex]\( 314 \text{ cm}^2 \)[/tex].
So the correct option is:
C. [tex]\( 314 \text{ cm}^2 \)[/tex]
