How To Calculate The Area Of A Circle When The Radius Is Given: A Step-by-Step Guide

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.