Real Life Applications of Circle Formula Properties and Solved Problems
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 Application of Circle in Mathematics with Real Life Examples
1. What are the applications of a circle in real life?
The applications of a circle in real life include designing wheels, gears, clocks, round tables, pipelines, and circular tracks. Circles are widely used because all points on a circle are equidistant from the center, which ensures balance and symmetry.
- Wheels and gears – smooth rotation and uniform motion.
- Architecture – domes, arches, circular windows.
- Engineering – pipes, tanks, circular plates.
- Astronomy – modeling planetary orbits (approximately circular).
2. What is the formula for the area of a circle and how is it used?
The area of a circle is calculated using the formula A = πr², where r is the radius. This formula helps find the space enclosed by a circle.
- Example: If r = 7 cm, then A = π × 7² = π × 49 = 154 cm² (using π = 22/7).
- Used in land measurement, flooring design, and circular object calculations.
3. How do you find the circumference of a circle?
The circumference of a circle is found using C = 2πr or C = πd, where r is the radius and d is the diameter. It represents the distance around the circle.
- Example: If r = 10 cm, then C = 2 × π × 10 = 20π ≈ 62.8 cm.
- Used in calculating fencing length, wheel rotation distance, and circular track length.
4. How is a circle used in solving real-life word problems?
A circle is used in word problems by applying formulas for area, circumference, arc length, or sector area depending on the situation. Identifying the given radius or diameter is the first step.
- Step 1: Identify what is given (radius/diameter).
- Step 2: Choose the correct formula.
- Step 3: Substitute values and calculate.
5. What is the application of sectors of a circle?
A sector of a circle is used to calculate portions of circular regions, such as slices of pizza or pie charts. The area of a sector is given by (θ/360°) × πr², where θ is the central angle.
- Example: If θ = 90° and r = 14 cm, Area = (90/360) × π × 14² = 154 cm².
- Used in statistics (pie charts) and engineering designs.
6. How is the concept of circle used in construction and architecture?
In construction and architecture, circles are used to design domes, arches, circular halls, and round pillars because they provide symmetry and strength. The uniform distance from the center ensures balanced load distribution.
- Domes distribute weight evenly.
- Circular columns resist pressure uniformly.
- Round layouts improve aesthetics and acoustics.
7. What is the difference between area and circumference of a circle?
The area of a circle measures the space inside it, while the circumference measures the distance around it.
- Area formula: A = πr² (square units).
- Circumference formula: C = 2πr (linear units).
- Example: For r = 7 cm, Area = 154 cm², Circumference = 44 cm.
8. How do you calculate the arc length of a circle?
The arc length of a circle is calculated using (θ/360°) × 2πr, where θ is the central angle in degrees. It represents a portion of the circumference.
- Example: If θ = 60° and r = 21 cm, Arc length = (60/360) × 2π × 21 = 22 cm (using π = 22/7).
- Used in track design and curved boundary measurement.
9. Why is the circle important in engineering and mechanics?
The circle is important in engineering because it ensures smooth rotational motion and equal force distribution from the center. Circular shapes reduce friction and maintain balance.
- Wheels rotate smoothly due to constant radius.
- Gears transfer motion efficiently.
- Pipes allow uniform fluid flow.
10. Can you give an example of a real-life problem involving a circle?
A common real-life example is finding the area of a circular garden to calculate grass cost using A = πr². Suppose the radius is 14 m.
- Area = π × 14² = π × 196 = 616 m² (using π = 22/7).
- If grass costs $5 per m², total cost = 616 × 5 = $3080.
