Introduction to the topic
Any plane figure enclosed by a curved line (such that all straight lines drawn from the center unto that curved line are the same in length) is called Circle. A circle is a closed 2-d flat figure. The circle is seen as a symbol of symmetry. Some daily life applications of the circle may be tyres, pizzas, rings, satellite’s orbits etc. The circle is an important geometrical concept. Circles have two main concepts, namely, Circumference and Area of circle, and these seem very well explained on the Cuemath app.
The measurement of the region that lies inside the curved line which is equidistant from the center at any point is known as the area for the circular region. Here, the concept of area for the circles is explained in detail.
Explaining important parts associated with circles
Any circle is a closed flat geometric shape formed with the collection of countless points equidistant from a fixed point inside the figure. Mostly, the concepts related to the circle depend on its corresponding parts. So, it becomes necessary to explore and understand the basic terms and parts of the circle.
- Radius: The measurement of the segment drawn from the exact middle to the boundary of the respective circle is the radius. The symbol of the radius is accepted as ‘r’ or ‘R’. The radius is important in finding out the circumference (perimeter) as well as the area of the same.
- Diameter: Any line segment going through the centre and touching the boundary at the endpoints is the diameter of the circle. It is given by the symbol ’d’ or ‘D’ and it is always twice the measurement of the radius.
- Circumference: The concept is explained as the measurement of the boundary of any circle or can also be understood as the concept of the perimeter of figures. Circumference= 2πr.
Exploring Area of the circle
The region that comes within the boundary of any circle (may it be a circular road, circular field, circular park or anything) is its area. It can also be defined as the total of the square units that lie in the circle.
The area of any circle can be calculated using radius, diameter or circumference. So, let’s get familiar with all the three methods of calculating the area of the same.
- Obtaining the area using the radius
The area of a circular shape can be easily found from its radius by using the basic relation,
Area of a circle, A=π×r^2
If the diameter is given, then one can easily obtain the radius (as the radius is ½ the length of the diameter) and then that is substituted in the above-mentioned relation to get the area of the circle.
- Obtaining the area using the diameter
The connection between the area and diameter can be shown by the relation
Area of circle=π/4×d^2
Usually, one first finds out the radius if the diameter of the circle is known. Then, obtain the area of the same by using relation in point 1 but using the above relation one can find out the area simply by using the diameter itself.
- Obtaining the area using the given circumference
Whenever the circumference is known, one opts to find the radius using the respective circumference and then the final area is obtained using that calculated radius in the relation given in point 1. There is one more method to solve the problem and that is by giving the concept directly in terms of circumference. The direct application of given circumference in a formula to get the required area of the figure is,
Area of the respective circle= (C^2)/4π, [C implies the circumference]
Derivation of the basic relation of the area i.e., Area=π×r^2
If any circle is partitioned into tiny sectors organised symmetrically it will form a rectangular parallelogram. When its area is calculated ½ circumference of the circle forms the length of the rectangle and the radius of the circle is the breadth of the rectangle. Finding the area of a rectangle, we get length× breadth=1/2× 2πr× r = π×r^2.
*π always is taken as 3.14 or 22/7.
The above-mentioned relations about the area of circles help understand the relationship between the parts of a circle and its bounded area. The topic is interesting and we’ll be explained by Cuemath experts.