Introduction
Kids, the circle is such a common shape that we encounter it practically everywhere we go, from packing a circle lunch box for the trip to school in the morning to eating circle-shaped cookies when you get home. Adults who look at a watch or bottle cap also notice this shape. Let's learn more about this interesting shape and its applications.
What is a Circle?
The term "circle" is derived from the Greek word "kirkos," meaning hoop or ring. A circle can be defined as a two-dimensional figure whose boundary consists of points equidistant from the centre of the circle. Many people believe that the circle is perfect. The circle is ideal because every line crossing its centre produces a reflection.
Circle
Applications of Circle
The fixed distance from the centre is called the circle's radius. The diameter of the circle is double its radius. The radius of a circle can be used to calculate the perimeter and area of a circle. We have seen many shapes that are round in shape in real life. The use of a circle starts from the pen's tip and ends with the planet's shape. Camera lenses, Ferris wheels, pizza, rings, steering wheels, pies, cakes, and buttons are examples of real-life circle applications.
Following are the Applications of the Area of a Circle in Daily Life
To find any cylinder's volume and surface area.
To find the surface area and volume of a cone.
To find the surface area and volume of a sphere.
For taking measurements of various circular figures.
Application of the Properties of Circle
The properties of a circle are:
If the radii of the circles are the same, the circles are said to be congruent.
The longest chord in a circle is its diameter.
Equal chords subtend equal angles at the centre of the circle.
The chord is always divided in half when the radius is drawn perpendicular to it.
Circles with different radii are never identical in size but are always similar.
Equal in length are the chords equally spaced from the centre.
The tangents are parallel if drawn at the diameter's end.
Questions Related To Circle
1. To find the length of the boundary of a cricket field what can be used?
Ans. The perimeter that can be found using the radius of the circular field.
2. To find the amount of material to be used for the carpeting of a circular room what can be used?
Ans. The area of the circular floor will be useful to estimate the amount of material that will be used for carpeting.
Conclusion
In this article, you have learnt the definition of circle and the origin of the word “circle”. You have learnt about the application of the circle and its uniqueness. You have also learnt various terms related to circle. You have also understood the application of circle theorems in real life. We hope you liked this article.
FAQs on Applications of a Circle
1. What are some key applications of a circle in everyday life?
Circles are fundamental in many real-world objects and systems. Key examples of their application include:
- Wheels and Gears: The most classic example, enabling transportation (cars, bicycles) and the function of machinery.
- Clocks and Watches: The hands of an analog clock trace a circular path to indicate the passage of time.
- Lenses and Optics: Lenses in cameras, glasses, and telescopes are typically circular to focus light uniformly to a single point.
- Architecture: Circular windows, arches, and domes are used for both their aesthetic appeal and their ability to distribute weight and stress evenly.
- Navigation: A compass uses a circular dial for direction, and GPS systems use circular ranges from satellites to pinpoint a location.
2. How is the concept of a circle used in engineering and technology?
In engineering, the properties of a circle are critical for design and function. The constant radius ensures uniform and predictable rotation in motors, engines, and turbines. In telecommunications, the broadcast area of an antenna is often modelled as a circle, defining its signal range. In robotics, the path and reach of robotic arms are calculated using principles of circular arcs and angles.
3. What is the fundamental definition of a circle as per the NCERT syllabus?
As per the NCERT syllabus, a circle is defined as the locus (or set) of all points in a plane that are at a fixed distance from a single fixed point. The fixed point is called the centre, and the fixed distance is called the radius. This simple definition is the foundation for all of its complex properties and diverse applications.
4. Why is a circle often considered the most efficient shape for certain applications?
A circle is highly efficient due to its unique geometric properties. For a given perimeter, a circle encloses the maximum possible area, making it the ideal shape for pipes, tunnels, and containers to maximise flow or volume. Furthermore, it has no corners (vertices), which means stress is distributed evenly along its circumference. This gives it great structural strength against internal or external pressure, as seen in submarine windows, storage tanks, and manhole covers.
5. How do mathematical concepts like tangents and the area of a circle apply to real-world problems?
These concepts from the CBSE syllabus are used to solve practical problems. For example:
- Tangents: The path of a rope unwinding from a spool or the straight line of sight from a person to a large spherical object (like the horizon on Earth) is a tangent. This principle is crucial in physics and engineering for calculating motion and sightlines.
- Area (πr²): This formula is used to calculate the amount of material needed for a circular tabletop, the land area covered by a circular irrigation sprinkler, or the cross-sectional area of a wire to determine its current-carrying capacity.
6. How are circles applied in other fields of Mathematics, such as trigonometry and coordinate geometry?
Circles are a unifying concept across different mathematical disciplines. In trigonometry, the 'unit circle' is the foundation for defining trigonometric functions like sine, cosine, and tangent for all angles. In coordinate geometry, a circle is represented by an equation, such as (x - h)² + (y - k)² = r², which allows us to model and analyse circular paths and shapes algebraically. This is essential for modern applications like computer graphics, satellite orbits, and physics simulations.
7. Beyond wheels, what are some less obvious but critical applications of circles in science?
A common misconception is limiting the application of circles to just wheels. However, some of its most powerful applications are less visible. For example, the orbits of planets and moons are often approximated as circles in initial calculations. In physics, the propagation of waves (like light or sound) from a point source spreads out in concentric circles. Even at a microscopic level, the cross-section of a fibre optic cable is circular to ensure efficient internal reflection of light signals.
