Area of a Circle

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Lesson Objective

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

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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.

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Study Tips

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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 explanation on this. Also, we will see some examples on how to use this formula.

a circle

Math Video

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Lesson Video

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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.

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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.

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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.

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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

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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.

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Please feel free to visit the Q&A Library. You can read the Q&As listed in any of the available categories such as Algebra, Graphs, Exponents and more. Also, you can submit math question, share or give comments there.

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