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Area of a Circle – How to Calculate Area and Circumference of a Circle?

ByDave Stopher

Feb 24, 2021

Kids start to learn about circles during elementary or primary school. While proceeding to higher-grades, they study more complex concepts based on it. By middle school, kids study the topic of geometry, which includes working with various properties of circles like finding the area of circle, the radius of the circle, circumference, diameter, etc.

Kids in higher grades also need to study various word problems based on circles and their properties. This makes it extremely crucial for kids to learn circles to implement their comprehensive knowledge and to the co-related topics and their applications. The topic of circles also holds great significance in our everyday life.

The word circle comes from the Greek word krikos, which means ring. It is a circular arc formed by tracing a point on a plane equidistant from the other point called the center of the circle. The length of this arc is known as the circumference or perimeter of a circle.

The utilization of circles is widely observed in several fields, ranging from the simplest to advanced mathematical calculations, science, architecture, etc. Some of the real-world examples of circles are wheels, rings, pizzas, donuts, etc. The symmetric properties of circles are often used to design athletic tracks, buildings, watches, wheels, and so on.

Definition of a Circle:

A circle is a basic geometric shape. It is a 2-dimensional representation of a sphere on a plane. This boundary of the circle is known as the circumference of the circle. A point equidistant from any other point located on the boundary of the circle is called the center of the circle. The line joining the center of the circle to any point on its circumference is known as its radius. A line passing through the center of the circle with endpoints on the boundary of the circle is called its diameter.

What is the Area of Circle?

The area enclosed in the boundary of the circle is called the surface area of a circle. It is widely used in real-life to calculate the area of objects which are circular like circular plot, race tracks, etc. We can easily calculate the surface area of a circle when the length of its radius, diameter, or circumference is known. The surface is calculated in squares units, using the formula πr².

How to Calculate the Area of a Circle?

We can calculate the area of a circle by using the following formulas:

  • Area = π x r², in terms of the radius ‘r’.
  • Area = (π/4) xd², in terms of the diameter ‘d’.
  • Area = C² / (4 π ), in terms of the circumference of the circle.

Example:

Let’s learn to calculate the area of a pizza. A large pizza area with a diameter of 16 inches. If the diameter of a large pizza is 16 inches, then its radius is 8 inches. Therefore the area of the large pizza will be π× 8² = 64π.

Circumference of Circle:

The circumference or perimeter of a circle is a boundary line with some distance from the center of the circle. It is the length of a complete arc of a circle. Out of all the shapes with the same area, a circle always has the smallest perimeter. The formula used to calculate the perimeter of a circle is ‘2πr’ where ‘r’ denotes a circle radius.

How to Calculate the Perimeter of a Circle?

We can calculate the perimeter of circle using the following formula:

  • Perimeter C = 2π x r, in terms of the radius ‘r’.
  • Perimeter C = π x d, in terms of the radius ‘d’.

Example: Let’s learn to calculate the circumference of a circular cake with a radius of 8cm. Perimeter C = 2π x r, Therefore the perimeter of the cake will be π× 8 = 8π.

Conclusion:

The topic of circles holds great significance in mathematics and studying the basics of this topic requires a deep understanding of all the concepts. Sound conceptual knowledge of each topic allows children to develop connections between various math topics, forming a strong math foundation. Cuemath helps kids to understand math logically by strengthening their reasoning skills to gain an in-depth understanding of each topic.