Area of a Circle

Lesson Objective

In this lesson, we will learn about the area of a circle.

About This Lesson

In this lesson, we will:

Learn about the formula for the area of a circle
See an example on using the formula to find a circle's area
See another example on using the formula to find the radius of a circle.

The study tips and math video below will explain more.

Study Tips

Tip #1

Consider the circle on the right, if the radius of this circle is r, the area, A of the circle will be:

A = πr²

where π is a constant that is approximately equals to 3.14.

The math video below will give more explanations on this. Also, we will see some examples on how to use the formula.

Math Video

Lesson Video

If the above player doesn't work, try this direct link.

Math Video Transcript

00:00:03.160
In this lesson, we will learn about the area of a circle.

00:00:07.220
Consider this circle with the radius r.

00:00:11.110
Now, the formula for the area of a circle, A, is pi r square, where PI, is a constant that is approximately equals to 3.14.

00:00:22.100
Note that, it is very important to include the unit. Since this is the formula for area, its unit will be in the form of square unit.

00:00:31.210
We will see more explanations on this, in the upcoming example.

00:00:37.060
Now, let's see some examples on using this formula. For these examples, we take pi as 3.14.

00:00:47.090
Find the area of this circle when its radius is 3cm.

00:00:52.160
To solve this, we start with the formula for the area of a circle, A equals to pi r square.

00:00:59.220
Since the radius is given as 3cm, we can substitute r with 3.

00:01:06.110
Next, we can simplify 3 square. 3 square is actually 3 multiply by 3. Which is equals to 9.

00:01:16.180
Let's write down this number.

00:01:19.240
Next, since PI is given as 3.14, we can substitute this pi with 3.14.

00:01:28.030
Let's continue by multiplying 3.14 with 9. This gives 28.26.

00:01:36.140
Note that, this number has no meaning unless we include the unit for it.

00:01:41.190
Since the radius is given in centimeter, the unit for the area will be in square centimeter.

00:01:48.010
Hence, the area of this circle is 28.26 square centimeter.

00:01:55.230
Next example, given that the area of this circle is 78.5 square feet. Find its radius.

00:02:04.180
Again, we start with the formula for the area of a circle, A equals to PI r square.

00:02:11.030
Now, since the values for A and PI are given, we can find the radius by solving this equation for r. Here’s how.

00:02:20.070
Since the value of the area is given as 78.5 square feet, we can substitute A with 78.5.

00:02:29.130
Similarly, since PI is given as 3.14, we can substitute this pi with 3.14.

00:02:37.180
Now we have 3.14 r square equals to, 78.5.

00:02:44.120
Let's rewrite this equation so that it will look neater.

00:02:48.130
To find r, we need to remove 3.14. We can do so by dividing both sides of the equation with 3.14.

00:02:58.210
After doing so, we have r square equals to 78.5 over 3.14.

00:03:05.220
78.5 divides by 3.14, gives 25.

00:03:11.210
Here, we have r square equals to 25. We can find 'r' by calculating the square root of 25.

00:03:21.060
Square root of 25 gives 5.

00:03:25.010
Now, this number is meaningless unless we include the unit for it.

00:03:29.220
Since the area is in square feet, the radius of the circle will be in feet.

00:03:35.160
Therefore, the radius of this circle is 5 ft.

00:03:40.130
That is all for this lesson. Try out the practice question to further your understanding.

Practice Questions & More

Multiple Choice Questions (MCQ)

Now, let's try some MCQ questions to understand this lesson better.

You can start by going through the series of questions on the area of a circle or pick your choice of question below.

Question 1 on finding the area of a circle
Question 2 on finding the radius of a circle

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