Perimeter Of a Circle

Title:-   Perimeter of a circle

Introduction:-

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The perimeter of a circle is an essential mathematical concept that plays a significant role in a range of fields. Most people have a basic understanding of what a circle is, but not everyone knows how to calculate its perimeter. In this article, I will discuss what the perimeter of a circle is, its formula, and real-world applications of this concept.

Explanation:-

To start this discussion, let us first know 

What is a circle?

Answer:- A round plane curved figure whose boundary (circumference) consists of points equidistant from a fixed point (the center) has no corners or edges is a two dimensional shape is called circle.

                     

In the picture,
        Center of the circle = P
   Radius of the circle = AP = PB = r
  Diameter of the circle = AB = d
Now we will learn

What is the Perimeter of a Circle?

Answer:-The perimeter of a circle is the distance around its edge or the length of its boundary. The circle is a two-dimensional shape that consists of all the points that are equidistant from a given point in a plane surface. The perimeter of a circle is also known as its circumference.

Formula for Calculating Perimeter of a Circle:-

P = 2πr …..(1)
or
   P =  πd…….(2)
Where P is the perimeter or circumference, and 'r' is the radius of the circle and d is the diameter of the circle. π is a mathematical constant that has a value of approximately 3.14 or 22/7.The radius is the distance from the center of the circle to any point on its boundary.

Using above formula, we can find the

perimeter of a semi circle:-

The perimeter of a semi circle can be given = ½ × perimeter of a circle + diameter of the circle
          = ½ × 2πr + d
          = πr + d, where r = Radius and d = Diameter of the circle.
To understand the formula better, let's consider an example. Suppose we have a circle with a radius of 50 cm. To calculate the perimeter (P) of the circle, we simply plug the value of the radius (r) into the formula above:
P = 2πr
P = 2 x 3.14 x 50
P = 314 cm
Therefore, the perimeter or circumference of the circle is 314 cm.

Some Problems related on Perimeter Of a Circle:-

Question(1):- The diameter of a circle is 21cm, Find its perimeter. (Take π = 22/7)

Answer:-  Diameter (d) = 21 cm
 ∴ perimeter of the circle = π × d
                                 = (22/7 × 21) cm
                                 = (22  × 3) cm
                                 = 66 cm

                                 

Question(2):- The radius of a circle is 50 m, find its perimeter.(Take π = 3.14)

Answer:-  Radius (r) = 50 m
 ∴ perimeter of the circle = 2π × r
                             =( 22 × 3.14  × 50)m
                             = (1100 × 3.14)m
                             = 3454 m

Question(3):- The perimeter of a circle is 88 cm, find its greatest chord. (Take, π = 22/7)

Answer:-   1st Method:-
 Perimeter of a circle = 88 cm
  ∴ Radius of the circle (r) = Perimeter / 2π
                            = 88 /( 2 × 22 /7)
                            = (88 × 7) / 2 × 22
                            = ( 88 × 7) / 44
                            = (2 × 7) cm
                            = 14 cm
∵ we know that the greatest chord of a circle is its diameter
∴ The greatest chord of the circle (diameter) = 2 × r
                 = (2 ×14) cm
                 = 28 cm

2nd Method:-
             
Perimeter of a circle = 88 cm
Let, the radius of the circle = r cm
Now,
According to question
        2π × r = 88
   =>  (2 × 22× r ) /7 = 88
   =>  r =(88 × 7) / 2 × 22
   =>  r = ( 88 × 7) / 44
   => r =  2 × 7
   => r = 14
∴ The radius of the circle = 14 cm
∵ we know that the greatest chord of a circle is its diameter
∴ The greatest chord of the circle (diameter) = 2 × r
                 = (2 ×14) cm
                 = 28 cm

Question (4) :- The radius of a semi circle is 7 cm, find its perimeter.

Answer:- Radius of the semi circle ( r ) = 7cm
   ∴ diameter of the circle (d) = 2 × r
                            = (2 × 7) cm
                            = 14 cm
∴ perimeter of the semicircle
       = π × r + d
       = (22/7 × 7) + 14
       = (22 + 14) cm
       = 36 cm

Real-World Applications of the Perimeter of a Circle:-

1 Construction Industry:-

The perimeter of a circle has variety of applications in the construction industry. Architects and construction engineers use this concept to calculate the perimeter of circular structures such as columns, towers, and walls. This knowledge enables them to determine the required length of the materials needed to complete the circular structure.

2. Science and Technology:-
The Perimeter Of a Circle has a significant role in various scientific fields such as physics and engineering. In physics, the knowledge of the perimeter of a circle is essentiall in calculating the circumference of a rotating wheel or a pulley system. In engineering, the concept is used in determining the perimeter of circular objects such as gears and turbines.

3. Transportation Industry:-
The Perimeter Of a Circle can be used in determining the distance traveled by vehicles such as cars and trains. This knowledge of the circumference allows engineers to calculate the rotation speed of vehicle tires, which is critical in determining fuel efficiency and tire wear.
4. Manufacturing Industry:-
The Perimeter Of a Circle is used in the manufacturing industry for the design and production of circular objects such as pipes, valves, and cables. Manufacturers need to know the exact length of these objects to cut or bend them to the required size.
5. Sports:-
The Perimeter Of a Circle is essential in various sports, such as athletics and basketball. In athletics, it is used to determine the distance traveled by an athlete running around a circular track. In basketball, the perimeter of the court is used to determine the distance between the three-point line and the basket.

Conclusion:-

In conclusion, the Perimeter Of a Circle is an essential concept in mathematics and has various applications in real-life situations. Its formula (P = 2πr) enables us to calculate the boundary of a circle accurately, which is useful both in theoretical and practical fields. From the construction industry to science and technology, transportation, manufacturing, and sports............

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FREQUENTLY ASKED QUESTIONs ON Perimeter Of a Circle:- 

 

Area of a circle

Answer:- Area of a circle = πr²,Where r = Radius of the circle and π = A special mathematical constant and is defined as the ratio between circumference to the diameter of the circle.

Perimeter of a semicircle

Answer:- The perimeter of a semi circle can be given = ½ × perimeter of a circle + diameter of the circle = ½ × 2πr + d = πr + d, where r = Radius and d = Diameter of the circle.

Circumference of a circle with radius.

Answer:- Circumference of a circle with radius = 2πr, where r = Radius of the circle.

Perimeter of rectangle

Answer :- Perimeter of rectangle = 2( l + b) where, l = length of the rectangle and b = breadth of the rectangle

Perimeter of triangle

Answer :- Perimeter of triangle = sum of three three different sides ( In case of scalene triangle) but in case of equilateral triangle it is 3 × side, as all three sides of an equilateral triangle are equal, also in case of isosceles triangle = 2 × equal sides + third side as any two sides of an isosceles are equal.

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