### 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:

^{2}

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

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

### Math Video

#### 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

#### Site-Search and Q&A Library

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