Circumference of a Circle

Introduction

Circumference of a circle is the length of the boundary In Geometry, one of the two-dimensional figures is the circle. The real-life applications of circles are worldwide, they thrive in the fields of architecture and sciences.

Some of the examples in real-life are, wedding rings, shirt buttons, steering wheels, eye lenses, giant wheels, tyres of vehicles, compact discs, etc.,

They have a diameter and radius. The radius varies from one circle to another. The diameter of the circle divides the circle into two halves called semicircles. If a circle is drawn on a plane divide the plane into two parts or regions, namely, interior and exterior parts. This two-dimensional figure has both the area and the circumference.

In this tutorial, we will learn about the definition of pi (π), circles and their circumference along with a few solved examples.

Circles

A two-dimensional figure which is a round shape with every point on its boundary equidistant from its centre is called a Circle. From the centre of the circle to any point in the boundary of the circle if a line segment is drawn then it is called the radius of the circle. It is denoted by r or R.

Unlike the radius, if both the endpoints of the line segment are connected to the boundary of a circle then it is called the chord of the circle. Among the many chords drawn in a circle, the largest chord is said to be the diameter of the circle. It is denoted by d or D.

To find the area of the circle we need to multiply the radius r of the circle with the pi value (π).

Note:

• The diameter of the circle is twice the radius of the circle,

  $$\mathrm{diameter= 2 × radius}$$

• The radius of the circle is half the value of the diameter of the circle,

  $$\mathrm{radius = \frac{diameter}{2}}$$

Circumference of a Circle

If the boundary of the circle is measured then that distance is said to be the circumference of the circle. The circumference is also called the Perimeter of the circle. In simple terms, circumference is the path that goes around the shape. It determines the length of the circle. If twice the radius or the diameter is multiplied then we get the circumference of the circle.

$$\mathrm{Circumference\: of\: the\: circle\:=2πr\: units}$$

$$\mathrm{or }$$

$$\mathrm{ πd\: units}$$

Definition of Pi

• The non - terminating decimal or say the irrational number is called Pi.

• It is represented by π.

• The numerical value of π = $\mathrm{\frac{22}{7}}$ = 3.141592653589793238...

  since circumference of the circle= πd

  $$\mathrm{π=\frac{Circumference\: of\: the\: circle}{d}}$$,

• It is the ratio of the circumference of the circle to the diameter of the circle.

Solved Examples

1)If the radius of the circular button is 0.21 cm then find the circumference of the button.

Answer:

Given:

The Radius of the circular button = 0.21 cm.

$$\mathrm{The\: Circumference\: of\: the\: circle=2πr\: units}$$

$$\mathrm{The\: circumference\: of\: the\: button=2×\frac{22}{7}×0.21}$$

$$\mathrm{=44×0.03}$$

$$\mathrm{=1.32 cm}$$

2)If the diameter of the Ferris wheel is 56 m then find the circumference of the Ferris wheel.

Answer:

Given:

The Diameter of the Ferris wheel = 56 m.

$$\mathrm{The\: Circumference\: of\: the\: circle=πd\: units}$$

$$\mathrm{Circumference\: of\: the\: Ferris\: wheel=\frac{22}{7}×56}$$

$$\mathrm{ =22×8 }$$

$$\mathrm{=176 m.}$$

3)Brad built a circular wheel out of thermocol for his son with a circumference of 220 cm. Find the diameter of the wheel.

Answer:

$$\mathrm{The\: Circumference\: of\: the\: circle=πd\: units}$$

$$\mathrm{The\: Circumference\: of\: the\: Ferris\: wheel=\frac{22}{7}×d}$$

$$\mathrm{220=\frac{22}{7}×d}$$

$$\mathrm{d=220 \times \frac{7}{22}}$$

$$\mathrm{The\: diameter\: of\: the\: wheel = 70 m.}$$

4)Zoy bought a hula hoop whose circumference is 264 cm. Find the radius of the hula hoop.

Answer:

$$\mathrm{The\: Circumference\: of\: the\: circle=πd\: units}$$

$$\mathrm{The\: Circumference\: of\: the\: hula \: hoop=\frac{22}{7}×d}$$

$$\mathrm{264 =\frac{22}{7}×d }$$

$$\mathrm{d =264×\frac{7}{22}}$$

$$\mathrm{The\: diameter\: of\: the\: hula\: hoop = 84\: cm.}$$

$$\mathrm{The\: radius\: of\: the\: hula\: hoop\: =\frac{ diameter}{2}}$$

$$\mathrm{ =\frac{ 84}{2}}$$

The radius of the hula hoop = 42 cm.

5)If the radius of the circular ring is 35 cm then find the circumference of the ring.

Answer:

Given:

The Radius of the ring = 35 cm.

$$\mathrm{The\: Circumference\: of\: the\: circle=2πr\: units}$$

$$\mathrm{The\: circumference\: of\: the\: button=2×\frac{22}{7}×35 }$$

$$\mathrm{=44×5 }$$

$$\mathrm{=220\: cm.}$$

Conclusion

• A two-dimensional figure which is a round shape with every point on its boundary equidistant from its centre is called a Circle.

• From the centre of the circle to any point in the boundary of the circle if a line segment is drawn then it is called the radius of the circle.

• If both the endpoints of the line segment are connected to the boundary of a circle then it is called the chord of the circle.

• The largest chord in a circle is said to be the diameter of the circle.

• If the boundary of the circle is measured then that distance is said to be the Circumference or the Perimeter of the circle.

• Pi is the ratio of the circumference of the circle to the diameter of the circle and their numerical value is 3.141592653589793238....

FAQs

1. What is a Sphere?

Circles are two-dimensional shapes. If a circle is a three-dimensional figure as a round solid with every point on its surface equidistant from its centre then it is called a Sphere.

2. What is the difference between Plane and Solid figures?

• Plane figures are two-dimensional geometric objects. These types of shapes include Square, rectangle, circle, triangle, hexagon, octagon, pentagon, etc.

• Solid figures are three-dimensional geometric objects. These types of solid figures include cubes, cuboids, cylinders, cones, prisms, spheres, hemispheres, etc.

3. What is called the area and the volume of an object?

• The region of space occupied by a three-dimensional figure is called the volume of an object.

• The amount of space covered by a two-dimensional figure is called the area of an object.

4. What is a regular polygon?

In Euclidean geometry, a polygon is equiangular and has congruent sides.

E.g: square, rhombus, equilateral triangle.

A polygon with unequal sides is an Irregular polygon.

E.g: scalene triangle, parallelogram, isosceles triangle, rectangle, etc.

5. Name the types of Circle.

There are three types of Circles, namely, congruent circles, concentric circles, and tangent circles.

6. What is the standard equation of a circle

The general equation of a circle is given by,

$$\mathrm{(x-h)^2-(y-k)^2=r^2}$$

Where (h,k) is the coordinates of the circle's center and r is the radius of the circle.

7.Is a Circle a Polygon?

The surface of the plane, with a straight line, is said to be a polygon.

The boundary of the circle is curved and does not have a straight line. Therefore, a circle cannot be considered as a polygon.