Area of Circle

A circle is made up of small points that are all at the same distance from the fixed point which is also called a circle’s centre. A closed geometric shape is a circle. In everyday life, we see circles in the form of a wheel, pizzas, around the ground, and so on. The area of a circle is the calculation of the region enclosed within the given circle.

The radius of a circle is the distance between the centre and a point on the edge. 

The alphabet ‘r’ or ‘R’ is used to represent it. 

Radius is crucial in the formulas for calculating the area and circumference of a circle.

The diameter of a circle is a line that runs through the centre and has its endpoints on the circle. The letter ‘d’ or ‘D’ is used to represent the diameter of the circle. Diameter is twice the radius of the circle i.e. d = 2 r ,here r is termed as radius of the given circle.

A closed figure’s perimeter is equal to the length of its boundary. When it comes to circles, the circumference is referred to by a different name. The circle’s “Circumference” is what it’s termed. The circumference of a given circle is the length of the circle’s boundary. If we open the circle to produce a straight line, the circumference is the length of the straight line.

• Area of Circle: –

The area of a circle is the area covered or surrounded by its circumference. It is based on the square units of the measurement.

The area of any geometrical shape is its own. In a two-dimensional plane, this area is the region that encompasses the shape. Now we’ll look at the circumference of a circle. The area of a circle is defined as the area covered by one complete cycle of its radius on a two-dimensional plane.

A circle’s area is the amount of space that it takes up in a 2-D plane. The area of a circle is the space occupied within the boundary of a circle. The area of a circle is calculated using the formula A = πr2, where r is the radius of the circle. The square unit, such as m2, cm2, and so on, is the unit of area.

The area of a given circle is equal to πr2.

The circumference to diameter ratio of any circle is π (pi). It’s a mathematical constant that’s unique.

• Calculation of the area of Circle: –

We can derive the area of the circle by dividing the circles into sectors. Suppose that the circle is divided into 16 equal sectors, which are arranged in such a manner so that they can form a rectangular shape. The parallelogram-shaped figure formed by the sectors taken out of the circle will have the same area as the circle. Because the sectors are the same size, they will have the same arc length. Half of the circumference will be made up of red-colored sectors, while the other half will be made up of blue coloured sectors. The parallelogram will eventually appear like a rectangle with length equal to r and breadth equal to r if the number of sectors sliced from the circle is increased. Now we have a rectangular like figure whose length is πr and width is r.

Area of rectangular shape= length*width

=πr*r= πr2

Hence the area of the circle= Area of the rectangular shape= πr2.

• Area of Circle using diameter: –

The formula for the area of a circle in terms of diameter is: Area of a Circle = d2/4. The diameter of the circle is denoted by the letter ‘d.’ The diameter of a circle is equal to twice its radius. 2r = d in general, we need to find the radius of the circle first, then the area of the circle, starting with the diameter. We may find the area of the circle directly from the diameter of the circle using this formula.

• Application of area of Circle: –

Circles can be found in everyday life, both in nature and in man-made things. 

• The Manicouagan Reservoir in Canada is a ring-shaped lake that arose from the crater’s remains. 

• The bases of mushrooms with domed tops are round. 

• At amusement parks and carnivals, Ferris wheels raise the circle to vertical heights.

• Many domestic products have circled in their designs, such as cups, candles, and doorknobs.

The use of circles in architecture is common all around the world. Domes, such as those atop the United States Capital in Washington, D.C., the Duomo of the Florence Cathedral, and St. Peter’s Basilica in Vatican City, are all examples of architectural circles. Architects employ circles as decorative elements in their structures as well.

Conclusion: –

A circle is a geometric object defined as a locus of points on the plane that are all equidistant from one another. A series of arcs surrounds the centre point formed by the connected dots. Although there are no straight lines on a circle’s perimeter, straight lines are used in computations. A radius is a line that connects any point on the circle to the centre point. The circumference of the given circle is equal to its perimeter.

The area of a circle refers to the amount of space encompassed by a circle’s edge. The area occupied by the circle is the territory within the circle’s boundary. It’s also known as the total number of square units included within the circle.