Area of a Circle
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.
below will explain more.
Consider the circle on the right, if the radius of this circle is
, the area,
of the circle will be:
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.
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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. 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.
on finding the area of a circle
on finding the radius of a circle
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