The Circumference Formula is crucial in geometry, especially when dealing with circles and related shapes. This article dives deep into the concept of the circumference, its formula, and how it is applied to various geometric shapes. You'll also find practice problems to test your understanding and expand your knowledge.
Circumference Formula is given by the product of twice the radius and the constant value π. A circle is a two-dimensional curved figure and a bangle is one of the best examples of the Circle. In this article, we will learn about the Circumference Formula and also learn how to calculate the Circumference of a Circle using the Circumference Formula. We will also learn the Circumference Formula for semicircles, spheres, and other 3D objects whose at least one face is circular in nature.
Circumference Formula is a mathematical formula used to calculate the circumference of a circle which is also the perimeter of the circle. The Circumference Formula of a Circle is C = 2πr where 'r' is the radius of the circle or C = πd where d is the diameter of the circle. We can also say that the Circumference Formula is basically a mathematical equation to find the circumference of the circle.
Circumference Definition
The length of the boundary of a Circle is called the Circumference. The word Circumference is composed of two Latin Words Circum and Ferre. The word Circum means, around or about and Ferre means to carry. Hence, the word circumference means to carry around. For understanding, take a bangle and a thread. Put the thread around the circle in a closed manner. Now measure the length of this thread. The length of this thread will give you the measurement of the circumference of the Circle.
The use of thread is good at a beginner's level but not for the advanced stage. Hence, we need to learn the Circumference Formula for calculating the Circumference of the circle. Before learning the Circumference formula we should learn what is a Circle and what are its components.
What is a Circle?
A circle is two dimensional round shaped figure bounded by curved line. There are no edges or corner in a circle. The length of the curved line making the boundary of the circle is the circumference of the circle. The image showing the circle with all its components is attached below:
Components of Circle
There are the following components of a circle that define the nature of a circle.
Centre: Centre is the point inside a circle that is equidistant from the circumference of the circle.
Radius: The radius is the distance from the center of the circle to the circumference of the circle. A circle can have an infinite number of radii.
Diameter: Diameter is the length from one point on the circumference to another point passing through the center. The diameter is twice the length of the radius of the circle. A circle can have an infinite number of diameters.
Chord: The chord is the distance between any two points on the circumference of the circle. The diameter is the longest chord of the circle.
General Properties of Circle
Some general properties of circles are mentioned below:
- Circles with a common center are called Concentric Circles.
- Circles with the same radii measurement are congruent.
- The radius and tangent are perpendicular at the point of contact.
- A line segment from the radius and perpendicular to the chord bisects the chord.
Circumference of a circle is the length of the boundary surrounding the circle. The Circumference of a circle is equal to twice the product of the numerical constant π and the radius 'r'. The mathematical expression for Circumference Formula is given as follows:
If C is the circumference of the circle and r is the radius of the circle then, Circumference of the circle is given as
C = 2πr
If C is the Circumference of the circle and 'd' is the diameter of the circle then the Circumference of the Circle is given as
C = πd
where, d = 2r
In both the above formulas, the value of π is constant and equal to approximately 3.14 in decimal and 22/7 in fractional form. The exact value of π can't be found exactly. π is an irrational number.
Now one can think that if a semicircle is half of the circle then its circumference or perimeter would also be half of the circle. But that is actually wrong. If we see a semicircle, we see that arc is half of that of a circle but it is also enclosed by a line which is actually the diameter of the circle.
The formula for the circumference or perimeter of the semicircle is given by
Circumference of Semicircle = πr + 2r = 1/2(Circumference of Circle) + Diameter
where, r is the radius of the circle
Apart from the circle, the circumference can be calculated for some other curved objects. Lets's learn the circumference formula for cylinder, sphere, and ellipse.
A cylinder is a 3D object whose two ends consist of a flat circular plane and the middle region is a curved region along which the cylinder can roll. The circumference formula in the cylinder is used to find the circumference of the two circles at two ends. The circumference formula for the circular ends of a cylinder is given as
C = 2πr
where r is the radius of the cylinder
A sphere is a three-dimensional round-shaped object. Like a circle, it has also a center, radius, and boundary. The circumference of a sphere can be found along any axis i.e. x, y, and z as it is the same along all directions. The sphere circumference formula is given as
C = 2πr
where r is the radius of the sphere
The length of the boundary of an Ellipse is called its Circumference. We can't exactly calculate the circumference of an ellipse rather we can approximate it. Let's say an ellipse is defined by the equation (x2/a2) + (y2/b2) = 1 where a is the expansion of the ellipse along the x-axis and b is the expansion of the ellipse along the y-direction. If a is approximately equal to b then the expansion in both the x and y directions is the same and the ellipse will approximately become a circle. In this case, if a = b then the Circumference of the Ellipse is given by
C = π (a + b)
If a and b are not approximately equal then any other below formula can be used
C = π √[2(a2 + b2)]
C = π [ (3/2)(a + b) - √(ab) ]
Read More,
Problem 1: Calculate the circumference of a circle having a radius of 24 cm.
Solution:
Given,
The radius of the circle is 24 cm
We have
Circumference = 2πr
= 2 × 3.14 × 24
= 150.72 cm
Hence, the circumference of the circle is 150.72 cm.
Problem 2: Calculate the circumference of a circle having a radius of 25 cm.
Solution:
Given:
The radius of the circle is 25 cm
Circumference = 2πr
C = 2 × 3.14 × 25
C = 157 cm
Hence, the circumference of the circle is 157 cm.
Problem 3: Calculate the circumference of a circle having a radius of 7 cm.
Solution:
Given:
The radius of the circle is 7 cm
Circumference = 2πr
C = 2 × 3.14 × 7
C = 44 cm
Hence, the circumference of the circle is 44 cm.
Problem 4: Calculate the circumference of a circle having a radius of 12 cm.
Solution:
Given:
The radius of the circle is 12 cm
Circumference = 2πr
C = 2 × 3.14 × 12
C = 113.04 cm
Hence, the circumference of the circle is 113.04 cm.
Problem 5: Calculate the circumference of a circle having a radius of 42 cm.
Solution:
Given:
The radius of the circle is 42 cm
Circumference = 2πr
C = 2 × 3.14 × 42
C = 263.76 cm
Hence, the circumference of the circle is 263.76 cm.
Problem 6: If a circle is given having a length of a radius of 14 cm, how the circumference of the circle can be calculated?
Solution:
Circumference = 2πr
= 2 × 3.14 × 14
= 87.92 cm
Hence, the circumference of the circle is 87.92 cm
Q1: Using Circumference Formula, find the circumference of a circle of diameter 28 cm
Q2: What is the area of a circle if its circumference is 88 cm.
Q3: What is the circumference of a circle of a circle of radius 49 cm.
Q4: Find the ratio of diameter to circumference formula.
Q5: Find the ratio of Area to Circumference formula.
Q6: A circular garden has a radius of 21 meters. Calculate the length of fencing required to enclose it.
Q7: What is the area of a circle if its circumference is 132 cm?
Q8: Calculate the ratio of the diameter to the circumference of a circle.
Q9: Find the circumference of a circle that has an area of 154 square centimeters.
Q10: A cylinder has a radius of 8 cm. What is the circumference of its base?
Similar Reads
Maths Mathematics, often referred to as "math" for short. It is the study of numbers, quantities, shapes, structures, patterns, and relationships. It is a fundamental subject that explores the logical reasoning and systematic approach to solving problems. Mathematics is used extensively in various fields
5 min read
Basic Arithmetic
What are Numbers?Numbers are symbols we use to count, measure, and describe things. They are everywhere in our daily lives and help us understand and organize the world.Numbers are like tools that help us:Count how many things there are (e.g., 1 apple, 3 pencils).Measure things (e.g., 5 meters, 10 kilograms).Show or
15+ min read
Arithmetic OperationsArithmetic Operations are the basic mathematical operations—Addition, Subtraction, Multiplication, and Division—used for calculations. These operations form the foundation of mathematics and are essential in daily life, such as sharing items, calculating bills, solving time and work problems, and in
9 min read
Fractions - Definition, Types and ExamplesFractions are numerical expressions used to represent parts of a whole or ratios between quantities. They consist of a numerator (the top number), indicating how many parts are considered, and a denominator (the bottom number), showing the total number of equal parts the whole is divided into. For E
7 min read
What are Decimals?Decimals are numbers that use a decimal point to separate the whole number part from the fractional part. This system helps represent values between whole numbers, making it easier to express and measure smaller quantities. Each digit after the decimal point represents a specific place value, like t
10 min read
ExponentsExponents are a way to show that a number (base) is multiplied by itself many times. It's written as a small number (called the exponent) to the top right of the base number.Think of exponents as a shortcut for repeated multiplication:23 means 2 x 2 x 2 = 8 52 means 5 x 5 = 25So instead of writing t
9 min read
PercentageIn mathematics, a percentage is a figure or ratio that signifies a fraction out of 100, i.e., A fraction whose denominator is 100 is called a Percent. In all the fractions where the denominator is 100, we can remove the denominator and put the % sign.For example, the fraction 23/100 can be written a
5 min read
Algebra
Variable in MathsA variable is like a placeholder or a box that can hold different values. In math, it's often represented by a letter, like x or y. The value of a variable can change depending on the situation. For example, if you have the equation y = 2x + 3, the value of y depends on the value of x. So, if you ch
5 min read
Polynomials| Degree | Types | Properties and ExamplesPolynomials are mathematical expressions made up of variables (often represented by letters like x, y, etc.), constants (like numbers), and exponents (which are non-negative integers). These expressions are combined using addition, subtraction, and multiplication operations.A polynomial can have one
9 min read
CoefficientA coefficient is a number that multiplies a variable in a mathematical expression. It tells you how much of that variable you have. For example, in the term 5x, the coefficient is 5 — it means 5 times the variable x.Coefficients can be positive, negative, or zero. Algebraic EquationA coefficient is
8 min read
Algebraic IdentitiesAlgebraic Identities are fundamental equations in algebra where the left-hand side of the equation is always equal to the right-hand side, regardless of the values of the variables involved. These identities play a crucial role in simplifying algebraic computations and are essential for solving vari
14 min read
Properties of Algebraic OperationsAlgebraic operations are mathematical processes that involve the manipulation of numbers, variables, and symbols to produce new results or expressions. The basic algebraic operations are:Addition ( + ): The process of combining two or more numbers to get a sum. For example, 3 + 5 = 8.Subtraction (−)
3 min read
Geometry
Lines and AnglesLines and Angles are the basic terms used in geometry. They provide a base for understanding all the concepts of geometry. We define a line as a 1-D figure that can be extended to infinity in opposite directions, whereas an angle is defined as the opening created by joining two or more lines. An ang
9 min read
Geometric Shapes in MathsGeometric shapes are mathematical figures that represent the forms of objects in the real world. These shapes have defined boundaries, angles, and surfaces, and are fundamental to understanding geometry. Geometric shapes can be categorized into two main types based on their dimensions:2D Shapes (Two
2 min read
Area and Perimeter of Shapes | Formula and ExamplesArea and Perimeter are the two fundamental properties related to 2-dimensional shapes. Defining the size of the shape and the length of its boundary. By learning about the areas of 2D shapes, we can easily determine the surface areas of 3D bodies and the perimeter helps us to calculate the length of
10 min read
Surface Areas and VolumesSurface Area and Volume are two fundamental properties of a three-dimensional (3D) shape that help us understand and measure the space they occupy and their outer surfaces.Knowing how to determine surface area and volumes can be incredibly practical and handy in cases where you want to calculate the
10 min read
Points, Lines and PlanesPoints, Lines, and Planes are basic terms used in Geometry that have a specific meaning and are used to define the basis of geometry. We define a point as a location in 3-D or 2-D space that is represented using coordinates. We define a line as a geometrical figure that is extended in both direction
14 min read
Coordinate Axes and Coordinate Planes in 3D spaceIn a plane, we know that we need two mutually perpendicular lines to locate the position of a point. These lines are called coordinate axes of the plane and the plane is usually called the Cartesian plane. But in real life, we do not have such a plane. In real life, we need some extra information su
6 min read
Trigonometry & Vector Algebra
Trigonometric RatiosThere are three sides of a triangle Hypotenuse, Adjacent, and Opposite. The ratios between these sides based on the angle between them is called Trigonometric Ratio. The six trigonometric ratios are: sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).As give
4 min read
Trigonometric Equations | Definition, Examples & How to SolveTrigonometric equations are mathematical expressions that involve trigonometric functions (such as sine, cosine, tangent, etc.) and are set equal to a value. The goal is to find the values of the variable (usually an angle) that satisfy the equation.For example, a simple trigonometric equation might
9 min read
Trigonometric IdentitiesTrigonometric identities play an important role in simplifying expressions and solving equations involving trigonometric functions. These identities, which include relationships between angles and sides of triangles, are widely used in fields like geometry, engineering, and physics. Some important t
10 min read
Trigonometric FunctionsTrigonometric Functions, often simply called trig functions, are mathematical functions that relate the angles of a right triangle to the ratios of the lengths of its sides.Trigonometric functions are the basic functions used in trigonometry and they are used for solving various types of problems in
6 min read
Inverse Trigonometric Functions | Definition, Formula, Types and Examples Inverse trigonometric functions are the inverse functions of basic trigonometric functions. In mathematics, inverse trigonometric functions are also known as arcus functions or anti-trigonometric functions. The inverse trigonometric functions are the inverse functions of basic trigonometric function
11 min read
Inverse Trigonometric IdentitiesInverse trigonometric functions are also known as arcus functions or anti-trigonometric functions. These functions are the inverse functions of basic trigonometric functions, i.e., sine, cosine, tangent, cosecant, secant, and cotangent. It is used to find the angles with any trigonometric ratio. Inv
9 min read
Calculus
Introduction to Differential CalculusDifferential calculus is a branch of calculus that deals with the study of rates of change of functions and the behaviour of these functions in response to infinitesimal changes in their independent variables.Some of the prerequisites for Differential Calculus include:Independent and Dependent Varia
6 min read
Limits in CalculusIn mathematics, a limit is a fundamental concept that describes the behaviour of a function or sequence as its input approaches a particular value. Limits are used in calculus to define derivatives, continuity, and integrals, and they are defined as the approaching value of the function with the inp
12 min read
Continuity of FunctionsContinuity of functions is an important unit of Calculus as it forms the base and it helps us further to prove whether a function is differentiable or not. A continuous function is a function which when drawn on a paper does not have a break. The continuity can also be proved using the concept of li
13 min read
DifferentiationDifferentiation in mathematics refers to the process of finding the derivative of a function, which involves determining the rate of change of a function with respect to its variables.In simple terms, it is a way of finding how things change. Imagine you're driving a car and looking at how your spee
2 min read
Differentiability of a Function | Class 12 MathsContinuity or continuous which means, "a function is continuous at its domain if its graph is a curve without breaks or jumps". A function is continuous at a point in its domain if its graph does not have breaks or jumps in the immediate neighborhood of the point. Continuity at a Point: A function f
11 min read
IntegrationIntegration, in simple terms, is a way to add up small pieces to find the total of something, especially when those pieces are changing or not uniform.Imagine you have a car driving along a road, and its speed changes over time. At some moments, it's going faster; at other moments, it's slower. If y
3 min read
Probability and Statistics
Basic Concepts of ProbabilityProbability is defined as the likelihood of the occurrence of any event. It is expressed as a number between 0 and 1, where 0 is the probability of an impossible event and 1 is the probability of a sure event.Concepts of Probability are used in various real life scenarios : Stock Market : Investors
7 min read
Bayes' TheoremBayes' Theorem is a mathematical formula used to determine the conditional probability of an event based on prior knowledge and new evidence. It adjusts probabilities when new information comes in and helps make better decisions in uncertain situations.Bayes' Theorem helps us update probabilities ba
13 min read
Probability Distribution - Function, Formula, TableA probability distribution is a mathematical function or rule that describes how the probabilities of different outcomes are assigned to the possible values of a random variable. It provides a way of modeling the likelihood of each outcome in a random experiment.While a Frequency Distribution shows
13 min read
Descriptive StatisticStatistics is the foundation of data science. Descriptive statistics are simple tools that help us understand and summarize data. They show the basic features of a dataset, like the average, highest and lowest values and how spread out the numbers are. It's the first step in making sense of informat
5 min read
What is Inferential Statistics?Inferential statistics is an important tool that allows us to make predictions and conclusions about a population based on sample data. Unlike descriptive statistics, which only summarizes data, inferential statistics lets us test hypotheses, make estimates and measure the uncertainty about our pred
7 min read
Measures of Central Tendency in StatisticsCentral tendencies in statistics are numerical values that represent the middle or typical value of a dataset. Also known as averages, they provide a summary of the entire data, making it easier to understand the overall pattern or behavior. These values are useful because they capture the essence o
11 min read
Set TheorySet theory is a branch of mathematics that deals with collections of objects, called sets. A set is simply a collection of distinct elements, such as numbers, letters, or even everyday objects, that share a common property or rule.Example of SetsSome examples of sets include:A set of fruits: {apple,
3 min read
Practice