### Area of a Circle #### Lesson Objective

In this lesson, we will learn about the area of a circle. 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 explanation on this. Also, we will see some examples on how to use this formula. ### Math Video #### Lesson Video #### Math Video Transcript

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

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Consider this circle with the radius r.

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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.

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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.

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

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

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

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

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

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

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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.

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Let's continue by multiplying 3.14 with 9. This gives 28.26.

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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.

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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.

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

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

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

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Similarly, since PI is given as 3.14, we can substitute this pi with 3.14.

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Now we have 3.14 r square equals to, 78.5.

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Let's rewrite this equation so that it will look neater.

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

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After doing so, we have r square equals to 78.5 over 3.14.

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78.5 divides by 3.14, gives 25.

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

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Square root of 25 gives 5.

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Now, this number is meaningless unless we include the unit for it.

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Since the area is in square feet, the radius of the circle will be in feet.

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Therefore, the radius of this circle is 5 ft.

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

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. 