The measure of the space or region enclosed inside the circle is known as the area of the circle. Radius : The distance from the center to a point on the boundary is called the radius of a circle. It is represented by the letter 'r' or 'R'. Radius plays an important role in the formula for the area and circumference of a circle, which we will learn later. Diameter : A line that passes through the center and its endpoints lie on the circle is called the diameter of a circle.
It is represented by the letter 'd' or 'D'. Diameter formula: The diameter formula of a circle is twice its radius. Circumference: The circumference of the circle is equal to the length of its boundary. This means that the perimeter of a circle is equal to its circumference. The length of the rope that wraps around the circle's boundary perfectly will be equal to its circumference.
The below-given figure helps you visualize the same. The circumference can be measured by using the given formula:. The circumference of a circle can be used to find the area of that circle. Consider a circular-shaped park as shown in the figure below. We can identify the various parts of a circle with the help of the figure and table given below.
The area of a circle is the amount of space enclosed within the boundary of a circle. The region within the boundary of the circle is the area occupied by the circle. It may also be referred to as the total number of square units inside that circle. The area of a circle can be calculated in intermediate steps from the diameter, and the circumference of a circle. From the diameter and the circumference, we can find the radius and then find the area of a circle.
But these formulae provide the shortest method to find the area of a circle. Example1: If the length of the radius of a circle is 4 units. Calculate its area. Answer: The area of the circle is Example 2: The length of the largest chord of a circle is 12 units.
Find the area of the circle. Here 'd' is the diameter of the circle. The diameter of the circle is twice the radius of the circle. Generally from the diameter, we need to first find the radius of the circle and then find the area of the circle.
With this formula, we can directly find the area of the circle, from the measure of the diameter of the circle.
There are two simple steps to find the area of a circle from the given circumference of a circle. The circumference of a circle is first used to find the radius of the circle. This radius is further helpful to find the area of a circle.
But in this formulae, we will be able to directly find the area of a circle from the circumference of the circle.
The area of the circle can be conveniently calculated either from the radius, diameter, or circumference of the circle. Any of the values of pi can be used based on the requirement and the need of the equations.
The below table shows the list of formulae if we know the radius, the diameter, or the circumference of a circle. Thus K is in reality a function of height that multiples the real circumference to produce surface area. We need to try find out why does K change with respect to height — which at the same time, we will treat as a function of the radius.
Now, note that h is a linear function of the radius — or at least in our examples, the function is linear. Though this differ from our original established value, we need to keep in mind that cylinders have two circular faces. The formula yields the circumference of both circular faces. This verifies part fo our formula. Now, using the previous values for h, we can obtain x, and verify that this equation is true in absolutely every case:.
A negative height places the second circular face of the cylinder in a non-existent plane, eliminate this second face and leaving us with one circle, for a factor in the circumference formula.
We have found an equation that explains why do tridimensional objects yield circumferences increased by some constant factor despite having their circumferences equal to that of a circle with equal radius. Although spheres are not cylinders, there is a direct relationship between the surface area and the volume of spheres and cylinders, which is why it also works for spheres and for cones cones also have the same relationship with cylinders; that was discovered by Archimides.
Why would 2piR be a universal multiplier? Notify me of follow-up comments by email. Notify me of new posts by email. There's a book! It's a collection of over fifty of my favorite articles, revised and updated. It's interesting. It's good. You should buy it. Click the photo for a link to the amazon page, or this link for the ebook. Email Address.
Skip to content. Home About Faq. Q: Is darkness a wave the way light is a wave? What is the speed of dark? Q: Is it a coincidence that a circles circumference is the derivative of its area, as well as the volume of a sphere being the antiderivative of its surface area?
What is the explanation for this? Posted on February 9, by The Physicist. Email Print Facebook Reddit Twitter. This entry was posted in -- By the Physicist , Math. Bookmark the permalink. Joe says:. February 9, at pm. February 10, at pm. Try this. In the applet below we have a six-sided regular polygon.
Keep clicking on 'more' and note that as the number of sides gets larger, the polygon approaches being a circle. As the number of sides becomes infinitely large, it is, in fact, a circle.
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