how do you find the circumference of a circle
In Mathematics, the circumference of any shape defines the path or the purlieus that surrounds the shape. In other words, the circumference is likewise called the perimeter, which helps to place the length of the outline of any shape. As nosotros know, the perimeter and expanse of circle are the two important parameters of a circle. In this article, we will discuss the " Circumference of a circle " or "Perimeter of circumvolve" with its definition, formula, methods to discover the circumvolve's circumference with many solved examples.
Table of Contents:
- Circumference Meaning
- Formulas
- What is the Circumference of a Circumvolve?
- Methods to Discover the Circumference
- Solved Bug
- Practice Issues
- FAQs
Circumvolve's Circumference
Circumference of the circle or perimeter of the circumvolve is the measurement of the boundary of the circle. Whereas the area of circle defines the region occupied by information technology. If nosotros open a circle and make a straight line out of it, then its length is the circumference. It is usually measured in units, such as cm or unit of measurement m.
When we use the formula to calculate the circumference of the circle, and so the radius of the circle is taken into account. Hence, we need to know the value of the radius or the diameter to evaluate the perimeter of the circle.
Circumference of a Circle Formula
The Circumference (or) perimeter of circle = 2πR
where,
R is the radius of the circle
π is the mathematical abiding with an gauge (upwardly to two decimal points) value of 3.fourteen
Over again,
Pi (π) is a special mathematical constant; information technology is the ratio of circumference to diameter of whatever circle.
where C = π D
C is the circumference of the circumvolve
D is the diameter of the circle
For example: If the radius of the circle is 4cm then detect its circumference.
Given: Radius = 4cm
Circumference = 2πr
= 2 x iii.14 x iv
= 25.12 cm
Also, check:
- Secant Of A Circle
- Sector Of A Circle
- Circles Class nine
- Circles For Class 10
Area of a Circle Formula
Area of any circumvolve is the region enclosed by the circle itself or the space covered by the circle. The formula to find the surface area of the circle is;
A = πr2
Where r is the radius of the circle, this formula is applicative to all the circles with different radii.
Perimeter of Semi-Circle
The semi-circle is formed when we carve up the circumvolve into two equal parts. Therefore, the perimeter of the semi-circle also becomes half.
Hence, Perimeter = πr +2r
Expanse of Semi-Circle
Surface area of the semi-circumvolve is the region occupied past a semi-circle in a 2D plane. The area of the semi-circle is equal to one-half of the surface area of a circle, whose radii are equal.
Therefore, Area = πr2/2
Thus, we can ascertain three different formulas to find the perimeter of circle (i.due east. circumference of a circle).
Formula 1: When the radius of a circle is known.
Circumference of a circle = 2πr
Formula 2: When the diameter of a circumvolve is known.
Circumference = πd
Formula three: When the area of a circumvolve is known, we can write the formula to notice the perimeter of the circle as:
C = √(4πA)
Hither,
C = Circumference of the circumvolve
A = Area of the circle
Summary
| Circumference of Circle | 2πr |
| Expanse of circle | πr2 |
| Perimeter of semi-circle | πr + 2r |
| Expanse of semi-circle | πrtwo/2 |
Radius of a Circle
The distance from the centre to the outer line of the circle is chosen a radius. It is the most important quantity of the circumvolve based on which formulas for the area and circumference of the circumvolve are derived. Twice the radius of a circumvolve is called the bore of the circle. The diameter cuts the circumvolve into two equal parts, which is called a semi-circle.
What is the Circumference of Circumvolve?
The meaning of circumference is the distance around a circle or any curved geometrical shape. It is the ane-dimensional linear measurement of the boundary across whatsoever two-dimensional circular surface. Information technology follows the same principle backside finding the perimeter of any polygon, which is why calculating the circumference of a circleis also known equally the perimeter of a circle.
A circle is defined as a shape with all the points are equidistant from a indicate at the centre. The circle depicted beneath has its heart lies at point A.
The value of pi is approximately iii.1415926535897… and we use a Greek letter π (pronounced every bit Pi) to draw this number. The value π is a non-terminating value.
For circle A (as given beneath), the circumferenceand the diameter will exist-
In other words, the distance surrounding a circle is known as the circumference of the circle. The diameter is the distance across a circle through the centre, and information technology touches the two points of the circle perimeter.π shows the ratio of the perimeter of a circle to the diameter. Therefore, when y'all divide the circumference past the bore for any circumvolve, you obtain a value shut enough to π. This relationship can be explained by the formula mentioned below.
C/d = π
Where C indicates circumference and d indicates bore. A unlike fashion to put upwardly this formula is C = π × d. This formula is mostly used when the diameter is mentioned, and the perimeter of a circumvolve needs to be calculated.
Circumference to Bore
Nosotros know that the diameter of a circle is twice the radius. The proportion between the circumference of a circle and its diameter is equal to the value of Pi(π). Hence, nosotros say that this proportion is the definition of the constant π.
(i.e) C= 2πr
C= πd (Every bit, d = 2r)
If nosotros divide both sides past the diameter of the circle, we will get the value that is approximately close to the value of π.
Thus, C/d = π.
How to Find Circumference?
Method 1:Since it is a curved surface, nosotros tin can't physically measure the length of a circle using a scale or ruler. But this tin can be done for polygons like squares, triangles and rectangles. Instead, nosotros can measure the circumference of a circle using a thread. Trace the path of the circle using the thread and marking the points on the thread. This length can be measured using a normal ruler.
Method 2:An accurate style of knowing the circumference of a circumvolve is to summate it. For this, the radius of the circumvolve has to be known. The radius of a circle is the distance from the center of the circle and any point on the circle itself. The figure below shows a circle with radius R and middle O. The diameter is twice the radius of the circle.
Solved Examples on Perimeter of Circle
Instance 1:
What is the circumference of the circle with diameter 4 cm?
Solution:
Since the diameter is known to us, we tin can calculate the radius of the circle,
Therefore, Circumference of the Circumvolve = 2 10 3.14 x 2 = 12.56 cm.
Example 2:
Detect the radius of the circle having C = 50 cm.
Solution:
Circumference = fifty cm
As per formula, C = 2 π r
This implies, l = 2 π r
fifty/2 = 2 π r/2
25 = π r
or r = 25/π
Therefore, the radius of the circle is 25/π cm.
Example 3:
Find the perimeter of circle whose radius is 3 cm?
Solution:
Given: Radius = iii cm.
We know that the circumference or the perimeter of a circle is2πr units.
Now, substitute the radius value in the formula, we get
C = (two)(22/seven)(3) cm
C = 18.857 cm
Therefore, the circumference of circle is 18.857 cm.
Example iv:
Calculate the perimeter of circle in terms ofπ, whose diameter is 10m.
Solution:
Given: Diameter = 10m.
Hence, radius = diameter/2 = 10/ii = 5 k.
We know that, perimeter of circle =2πr units
C =2π(5) = 10π yard.
Therefore, the perimeter of circumvolve in terms ofπ, whose diameter x cm is 10π m.
Instance 5:
Find the perimeter and expanse of circle whose radius is 5 cm. [Note: π = iii.xiv]
Solution:
To find: Perimeter and area of circle.
Given that, Radius, r = five cm and π = 3.xiv
Every bit we know, the circumference (or) perimeter of a circle = 2πr units
The area of a circle = πrii foursquare units.
Now, substitute the values in the perimeter and expanse of circle formula, we get
The area of circumvolve = πrtwo = 3.14(5)2
A = 3.14(25)
A = 78.5 cmii
The circumference of a circumvolve = 2πr = 2(3.fourteen)(v)
Circumference = 3.14(10) = 31.4 cm.
Hence, the perimeter and area of circle are 31.4 cm and 78.5 cm2 respectively.
Practise Questions
- Summate the perimeter of circle whose bore is viii cm.
- What volition be the bore of a circumvolve if it'due south C = 10 cm?
- If C = 12 cm, what will be its radius?
- What is the circumference of a 16-inch circumvolve?
- What is the circumference of a 6 mm circle?
Scout The Below Video to Learn The Nuts of Circles
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Frequently Asked Questions
What is the Circumference of a Circle?
The circumference of a circle is defined equally the linear altitude effectually it. In other words, if a circle is opened to course a straight line, and then the length of that line will be the circumvolve's circumference.
How to Calculate the Circumference of a Circle?
To calculate the circumference of a circle, multiply the bore of the circle with π (pi). The circumference can also exist calculated by multiplying 2×radius with pi (π=3.14).
How to Calculate Diameter from Circumference?
The formula for circumference = diameter × π
Or, bore = circumference/π
So, the diameter of the circle in terms of circumference will be equal to the ratio of the circumference of the circle and pi.
What is the Circumference of a Circle with Radius 24 inches?
Circumference = ii×π×r
C = 2×iii.14×24
C = 150.72 inches
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