The area the a one is the space occupied through the one in a two-dimensional plane. Alternatively, the room occupied within the boundary/circumference of a circle is dubbed the area the the circle. The formula because that the area that a one is A = πr2, where r is the radius of the circle. The unit that area is the square unit, for example, m2, cm2, in2, etc. Area of one = πr2 or πd2/4 in square units, where (Pi) π = 22/7 or 3.14. Pi (π) is the proportion of circumference come diameter of any circle. That is a special mathematical constant.

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The area the a one formula is advantageous for measure up the an ar occupied through a circular field or a plot. Suppose, if you have a one table, then the area formula will aid us come know just how much towel is essential to cover the completely. The area formula will certainly also help us to know the boundary length i.e., the circumference of the circle. Go a circle have volume? No, a one doesn't have actually a volume. A circle is a two-dimensional shape, it does not have volume. A circle only has actually an area and also perimeter/circumference. Allow us discover in detail about the area the a circle, surface area, and its circumference through examples.

1.Circle and also Parts that a Circle
2.What Is the Area of Circle?
3.Area of one Formulas
4.Derivation of Area that a one Formula
5.Surface Area of one Formula
6.Real-World example on Area of Circle
7.FAQs top top Area that Circle

Circle and Parts the a Circle


A one is a arsenal of point out that are at a fixed distance native the center of the circle. A one is a closeup of the door geometric shape. We view circles in day-to-day life such as a wheel, pizzas, a circular ground, etc. The measure of the room or an ar enclosed within the one is known as the area the the circle.

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Radius: The street from the center to a suggest on the border is dubbed the radius of a circle. That is represented by the letter 'r' or 'R'. Radius plays an essential role in the formula because that the area and also circumference the a circle, which us will learn later.

Diameter: A line the passes v the center and its endpoints lie on the circle is dubbed the diameter the a circle. That is represented by the letter 'd' or 'D'.

Diameter formula: The diameter formula the a circle is double its radius. Diameter = 2 × Radius

d = 2r or D = 2R

If the diameter that a circle is known, the radius have the right to be calculate as:

r = d/2 or R = D/2

Circumference: The one of the circle is equal to the size of the boundary. This method that the perimeter the a circle is same to that circumference. The length of the rope that wraps approximately the circle's border perfectly will be equal to that is circumference. The below-given figure helps friend visualize the same. The circumference have the right to be measure up by utilizing the given formula:

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where 'r' is the radius of the circle and also π is the mathematical consistent whose value is approximated to 3.14 or 22/7. The circumference of a circle can be offered to find the area of the circle.

For a circle through radius ‘r’ and circumference ‘C’:

π = Circumference/Diameterπ = C/2r = C/dC = 2πr

Let us know the different parts of a circle using the following real-life example.

Consider a circular-shaped park as displayed in the number below. We have the right to identify the various parts of a circle through the help of the figure and also table offered below.

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In a CircleIn ours parkNamed through the letter
CentreFountainF
CircumferenceBoundary
ChordPlay area entrancePQ
RadiusDistance native the fountain come the entrance gateFA
DiameterStraight heat Distance between Entrance Gate and also Exit Gate v the fountainAFB
Minor segmentThe smaller area the the park, which is presented as the beat area
Major segmentThe larger area the the park, other than the pat area
Interior component of the circleThe eco-friendly area of the whole park
Exterior component of the circleThe area outside the border of the park
ArcAny curved part on the circumference.

The area the a circle is the quantity of an are enclosed in ~ the boundary of a circle. The region within the border of the one is the area inhabited by the circle. The may likewise be referred to as the total number of square devices inside that circle.


The area of a circle can be calculate in intermediate procedures from the diameter, and the circumference of a circle. From the diameter and also the circumference, we can find the radius and then uncover the area of a circle. However these formulae provide the shortest an approach to discover the area of a circle. Intend a circle has a radius 'r' then the area of circle = πr2 or πd2/4 in square units, where π = 22/7 or 3.14, and also d is the diameter.

Area of a circle, A = πr2 square units

Circumference / Perimeter = 2πr units

Area of a circle have the right to be calculated by using the formulas:

Area = π × r2, where 'r' is the radius.Area = (π/4) × d2, whereby 'd' is the diameter.Area = C2/4π, wherein 'C' is the circumference.

Examples making use of Area of circle Formula

Let us take into consideration the following illustrations based upon the area of circle formula.

Example1: If the size of the radius that a one is 4 units. Calculation its area.

Solution:Radius(r) = 4 units(given)Using the formula because that the circle's area,Area of a circle = πr2Put the values,A = π42A =π × 16A = 16π ≈ 50.27

Answer: The area that the circle is 50.27 squared units.

Example 2: The size of the biggest chord of a circle is 12 units. Discover the area the the circle.

Solution:Diameter(d) = 12 units(given)Using the formula because that the circle's area,Area the a circle = (π/4)×d2Put the values,A = (π/4) × 122A = (π/4) × 144A = 36π ≈ 113.1

Answer: The area the the one is 113.1 square units.

Area that a Circle utilizing Diameter

The area the the one formula in terms of the diameter is: Area the a circle = πd2/4. Here 'd' is the diameter that the circle. The diameter the the one is twice the radius the the circle. D = 2r. Typically from the diameter, we require to very first find the radius that the circle and also then find the area that the circle. With this formula, us can directly find the area of the circle, native the measure of the diameter of the circle.

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Area that a Circle making use of Circumference

The area the a one formula in regards to the one is offered by the formula (dfrac(Circumference)^24pi). There room two basic steps to uncover the area the a circle from the provided circumference the a circle. The one of a circle is an initial used to find the radius the the circle. This radius is further valuable to discover the area of a circle. However in this formulae, us will be able to directly uncover the area the a circle from the circumference of the circle.

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Area the a Circle-Calculation

The area that the circle can be conveniently calculated one of two people from the radius, diameter, or one of the circle. The constant used in the calculate of the area that a one is pi, and it has a fountain numeric worth of 22/7 or a decimal worth of 3.14. Any kind of of the values of pi deserve to be used based upon the requirement and also the need of the equations. The below table shows the list of formulae if we recognize the radius, the diameter, or the one of a circle.

Area the a circle once the radius is known.πr2
Area the a circle as soon as the diameter is known.πd2/4
Area that a circle when the circumference is known.C2/

Why is the area that the one is πr2? To know this, let's first understand exactly how the formula for the area of a one is derived.

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Observe the over figure carefully, if we break-up up the circle right into smaller sections and arrange them systematically it forms a form of a parallelogram. Once the circle is split into even smaller sectors, it slowly becomes the form of a rectangle. The an ext the variety of sections the has an ext it tends to have actually a shape of a rectangle as shown above.

The area of a rectangle is = size × breadth

The breadth the a rectangle = radius the a one (r)

When us compare the size of a rectangle and the one of a circle we have the right to see the the size is = ½ the circumference of a circle

Area of one = Area that rectangle developed = ½ (2πr) × r

Therefore, the area the the circle is πr2, whereby r, is the radius that the circle and also the value of π is 22/7 or 3.14.


The surface ar area the a circle is the exact same as the area the a circle. In fact, when we speak the area the a circle, we mean nothing but its complete surface area. Surface ar area is the area occupied by the surface ar of a 3-D shape. The surface of a sphere will be spherical in shape yet a one is a basic plane 2-dimensional shape.

If the length of the radius or diameter or also the circumference of the one is given, then us can discover out the surface area. That is represented in square units. The surface ar area of circle formula = πr2 where 'r' is the radius the the circle and the worth of π is about 3.14 or 22/7.


Ron and also his friend ordered a pizza on Friday night. Each slice was 15 centimeter in length.

Calculate the area of the pizza the was ordered by Ron. You have the right to assume that the length of the pizza slice is equal to the pizza’s radius.

Solution:

A pizza is one in shape. So we have the right to use the area the a circle formula to calculate the area that the pizza.

Radius is 15 cm

Area of one formula = πr2 = 3.14 × 15 × 15 = 706.5

Area that the Pizza = 706.5 sq. Cm.


Example 4: A wire is in the shape of an it is provided triangle. Each side the the triangle measures 7 in. The wire is bent right into the form of a circle. Find the area the the circle the is formed.

Solution:

Perimeter that the it is intended Triangle: Perimeter the the triangle = 3 × side = 3 × 7 = 21 inches.

Since the perimeter that the it is provided triangle = circumference of the circle formed.

Thus, the perimeter that the triangle is 21 inches.

Circumference of a one = 2πr = 2 × 22/7 × r = 21. R = (21 × 7)/(44) = 3.34.

Therefore, the Radius of the circle is 3.34 cm. Area the a one = πr2 = 22/7 ×(3.34)2 = 35.042 square inches.

Therefore, the area of a circle is 35.042 square inches.


Example 5: The time shown in a circular clock is 3:00 pm. The size of the minute hand is 21 units. Find the distance traveled by the tip of the minute hand once the time is 3:30 pm.

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Solution:

When the minute hand is at 3:30 pm, it covers fifty percent of the circle. So, the street traveled by the minute hand is actually fifty percent of the circumference. Distance (= pi) (where r is the length of the minute hand). Therefore the distance covered = 22/7 × 21 = 22 × 3 = 66 units. Therefore, the distance traveled is 66 units.