Home Middle-School Math: All About Circles

# Middle-School Math: All About Circles

Middle school math students meet some familiar faces in their geometry classes. They are reintroduced to all the shapes they learned in pre-school, but this time around, the information they can learn about the shapes and the way in which they learn to use these shapes improves significantly.

As well as all the knowledge they will gain about triangles when studying trigonometry, students will be taught how to measure different shapes, including the one that is the focus of this article: the circle.

From the wheels on our bikes to the plates we eat from, circles are an important part of everyday life. In middle school, students are charged with measuring things like the radius and diameter of a circle, its circumference, its area, and the area of a particular part of the circle. They will even learn about one of the most interesting concepts in geometry that relate to circles – pi.

All of these properties can be found quite easily, so let’s dive in and see how.

## Radius and diameter of a circle

As we know, a circle is a round, two-dimensional shape where all points are the same distance from the center. This distance between the center point of a circle and any point along the circle is called the radius. We denote the radius with the letter (r).

Now that we have the radius, our next step is to find the diameter of our circle. The diameter is the distance across the circle from one point to another that passing through the center of the circle. Since we know that the center point to any point along the circle is (r), we can say that the diameter (d) is equal to 2r.

Therefore, we can say d = 2r. This relationship between radius and diameter is crucial to calculating other properties of the circle, so make sure you learn this short equation well.

The diameter (d) of a circle is the distance across the circle passing through the center point and is equal to twice the radius (d = 2r). Understanding the relationship between the radius and diameter is crucial in calculating other properties of circles.

## Circumference of a circle

Next up, we have the circumference, which we denote with the letter (c). The circumference is the distance around the circle’s edge. To find the circumference, we need to rely on our old friend pi.

As we know from previous articles, pi is roughly equal to 3.14. Pi (π) is a mathematical constant that represents the ratio of a circle’s diameter to its circumference.

To find the circumference, we simply multiply our diameter by pi, leaving us with the equation C = πd. If we did not know the diameter of the circle, but we did know the radius, we could rewrite the equation as 2πr, because we know 2r is the same as d.

## Area of a circle and the area of a semicircle

Now that we have identified and found out how to measure the lengths around, across, and inside our circle, we need to figure out the area. When talking about circles, the area (A) represents the amount of space inside of the circle.

Once again, to find this answer, we will turn to our pal pi.

The equation to find the area of a circle is the radius of our circle squared, then multiplied by π. We can write the equation as A = πr2.

But what if we want to find the area of a particular part of our circle? Let’s take a look at an example, where we want to find the area of a semicircle, which is half of a circle.

If we know the radius is 2, we know that the area of the entire circle will be:

However, this is the area of the entire circle. We want to find the area of half of the circle. Therefore, we simply divide our answer by 2 and we have the area of our semicircle. In this case, the answer is 2π units2.

A = πr2 units2
A = π(2)2 units2
A = (4)π units2
A = 4π units2

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Contact OMC today to enroll your child in our tutoring classes and watch their geometry skills transform.

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