To find the area of a circle with a diameter of 10 cm, you can follow these steps:

Step 1: Recall the formula for the area of a circle.

The formula for the area $A$ of a circle is: $A = \pi r^2$ where $r$ is the radius of the circle.

Step 2: Find the radius of the circle.

The radius $r$ is half of the diameter. Since the diameter is 10 cm: $r = \frac{10}{2} = 5 \text{ cm}$

Step 3: Substitute the radius into the formula.

Now substitute $r = 5$ cm into the area formula: $A = \pi (5)^2$

Step 4: Simplify the expression.

Calculate $5^2$, which is 25: $A = \pi \times 25$

Step 5: Approximate using $\pi \approx 3.14159$.

$A \approx 3.14159 \times 25$ $A \approx 78.54 \text{ cm}^2$

Final Answer:

The area of the circle is approximately: $78.54 \text{ cm}^2$

Would you like more details or have any questions?

Here are some related questions:

1. What is the circumference of a circle with a diameter of 10 cm?
2. How would the area change if the diameter doubled to 20 cm?
3. What is the formula for the circumference of a circle and how is it related to the area?
4. How can we calculate the area if only the circumference is known?
5. What is the relationship between the radius and the area in terms of proportionality?

Tip: Remember, the area of a circle scales with the square of the radius, so doubling the radius quadruples the area!