Calculating the area of a circle is a fundamental concept in geometry. If you know the radius of the circle, determining its area is straightforward. This guide will walk you through the process step by step.
Step 1: Understand the Formula
The area (\(A\)) of a circle is calculated using the formula:
\[ A = \pi r^2 \]
where:
- \( A \) is the area
- \( r \) is the radius of the circle
- \( \pi \) (Pi) is approximately 3.14159
Step 2: Use Real Numbers for Calculation
Let's use a real example to make the calculation clear. Suppose the radius (\( r \)) of the circle is 7 units.
Step 3: Plug the Radius into the Formula
Now, substitute the radius value into the formula:
\[ A = \pi r^2 \]
\[ A = \pi \times 7^2 \]
Step 4: Calculate the Square of the Radius
First, calculate the square of the radius:
\[ 7^2 = 49 \]
So the equation becomes:
\[ A = \pi \times 49 \]
Step 5: Multiply by Pi
Next, multiply by Pi (\( \pi \)):
\[ A = 3.14159 \times 49 \]
Step 6: Perform the Multiplication
Now, perform the multiplication to find the area:
\[ A = 3.14159 \times 49 = 153.938 \, \text{square units} \]
So, the area of the circle is 153.938 square units.
Summary
To summarize, the steps to calculate the area of a circle when the radius is known are:
1. Use the formula \( A = \pi r^2 \).
2. Substitute the radius into the formula.
3. Calculate the square of the radius.
4. Multiply the result by Pi.
Using our example, with a radius of 7 units, we found the area of the circle to be 153.938 square units.
By following these steps, you can easily calculate the area of a circle for any given radius.
