The area the a one is the an are occupied by the circle in a two-dimensional plane. Alternatively, the room occupied within the boundary/circumference that a one is referred to as the area of the circle. The formula because that the area that a one is A = πr2, whereby r is the radius the the circle. The unit of area is the square unit, for example, m2, cm2, in2, etc. Area of circle = πr2 or πd2/4 in square units, whereby (Pi) π = 22/7 or 3.14. Pi (π) is the proportion of circumference come diameter of any kind of circle. The is a unique mathematical constant.

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

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

Circle and also Parts the a Circle

A circle is a collection of clues that room at a fixed distance indigenous the center of the circle. A one is a close up door geometric shape. We view circles in everyday life such together a wheel, pizzas, a one ground, etc. The measure of the room or region enclosed inside the circle is well-known as the area the the circle.


Radius: The street from the center to a allude on the boundary is referred to as the radius of a circle. It is stood for by the letter 'r' or 'R'. Radius plays an essential role in the formula because that the area and circumference that a circle, which we will learn later.

Diameter: A line the passes with the center and also its endpoints lied on the one is referred to as the diameter of a circle. It is stood for by the letter 'd' or 'D'.

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

d = 2r or D = 2R

If the diameter the a one is known, that radius have the right to be calculated as:

r = d/2 or R = D/2

Circumference: The one of the one is equal to the length of its boundary. This way that the perimeter the a one is same to the circumference. The length of the rope the wraps around the circle's border perfectly will certainly be equal to that circumference. The below-given figure helps friend visualize the same. The circumference deserve to be measured by making use of the given formula:


where 'r' is the radius the the circle and π is the mathematical continuous whose value is approximated to 3.14 or 22/7. The circumference of a circle have the right to be used to uncover the area of the circle.

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

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

Let us recognize the various parts that a circle making use of the adhering to real-life example.

Consider a circular-shaped park as displayed in the number below. We deserve to identify the assorted parts that a circle with the assist of the figure and table given below.


In a CircleIn our parkNamed by the letter
ChordPlay area entrancePQ
RadiusDistance indigenous the fountain come the enntrance gate gateFA
DiameterStraight line Distance in between Entrance Gate and Exit Gate with the fountainAFB
Minor segmentThe smaller area of the park, which is presented as the pat area
Major segmentThe enlarge area the the park, various other than the play area
Interior part of the circleThe green area that the entirety park
Exterior component of the circleThe area external the border of the park
ArcAny curved part on the circumference.

The area the a one is the quantity of an are enclosed within the boundary of a circle. The an ar within the border of the one is the area inhabited by the circle. That may additionally be described as the total variety of square devices inside that circle.

The area of a circle can be calculation in intermediate actions from the diameter, and the circumference of a circle. Native the diameter and also the circumference, we can find the radius and also then find the area the a circle. But these formulae carry out the shortest method to find the area the a circle. Expect a circle has actually a radius 'r' climate the area of circle = πr2 or πd2/4 in square units, whereby π = 22/7 or 3.14, and also d is the diameter.

Area that a circle, A = πr2 square units

Circumference / Perimeter = 2πr units

Area of a circle deserve to be calculation by utilizing the formulas:

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

Examples utilizing Area of one Formula

Let us take into consideration the following illustrations based on the area of one formula.

Example1: If the length of the radius that a circle is 4 units. Calculation its area.

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

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

Example 2: The size of the largest chord that a circle is 12 units. Find the area of the circle.

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

Answer: The area of the circle is 113.1 square units.

Area the a Circle using Diameter

The area of the one formula in terms of the diameter is: Area that a one = πd2/4. Below 'd' is the diameter of the circle. The diameter of the circle is double the radius the the circle. D = 2r. Typically from the diameter, we require to very first find the radius the the circle and then uncover the area that the circle. V this formula, us can straight find the area the the circle, indigenous the measure up of the diameter the the circle.


Area of a Circle making use of Circumference

The area of a circle formula in regards to the one is given by the formula (dfrac(Circumference)^24pi). There space two simple steps to find the area the a circle native the provided circumference that a circle. The circumference of a circle is very first used to find the radius the the circle. This radius is further useful to discover the area of a circle. However in this formulae, we will be able to directly discover the area the a circle native the circumference of the circle.


Area that a Circle-Calculation

The area the the circle can be conveniently calculated one of two people from the radius, diameter, or circumference of the circle. The continuous used in the calculation of the area of a circle is pi, and also it has a fractional numeric value of 22/7 or a decimal value of 3.14. Any kind of of the values of pi have the right to be used based upon the requirement and also the need of the equations. The below table reflects the list of formulae if we understand the radius, the diameter, or the one of a circle.

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

Why is the area of the circle is πr2? To understand this, let's an initial understand exactly how the formula because that the area that a one is derived.


Observe the over figure carefully, if we break-up up the circle into smaller sections and arrange castle systematically it develops a form of a parallelogram. Once the one is divided into even smaller sectors, it gradually becomes the form of a rectangle. The much more the number of sections that has much more it tends to have actually a form of a rectangle as presented above.

The area that a rectangle is = size × breadth

The breadth that a rectangle = radius the a circle (r)

When we compare the size of a rectangle and also the circumference of a circle we deserve to see the the size is = ½ the circumference of a circle

Area of circle = Area that rectangle formed = ½ (2πr) × r

Therefore, the area the the one is πr2, where r, is the radius of the circle and also the worth of π is 22/7 or 3.14.

The surface ar area that a circle is the very same as the area the a circle. In fact, once we say the area that a circle, we average nothing yet its complete surface area. Surface ar area is the area inhabited by the surface of a 3-D shape. The surface of a round will be spherical in shape but a one is a an easy plane 2-dimensional shape.

If the size of the radius or diameter or even the one of the one is given, then we can find out the surface area. The is represented in square units. The surface area of one formula = πr2 whereby 'r' is the radius of the circle and also the value of π is around 3.14 or 22/7.

Ron and his friend ordered a pizza ~ above Friday night. Each part was 15 centimeter in length.

Calculate the area of the pizza the was notified by Ron. You deserve to assume the the length of the pizza slice is same to the pizza’s radius.


A pizza is circular in shape. Therefore we deserve to use the area that a one formula to calculate the area that the pizza.

Radius is 15 cm

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

Area the the Pizza = 706.5 sq. Cm.

Example 4: A cable is in the form of an it is intended triangle. Every side the the triangle measures 7 in. The cable is bent into the form of a circle. Discover the area the the circle the is formed.


Perimeter of the it is intended Triangle: Perimeter of the triangle = 3 × next = 3 × 7 = 21 inches.

Since the perimeter of the it is intended triangle = circumference of the one formed.

Thus, the perimeter that the triangle is 21 inches.

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

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

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

Example 5: The time displayed in a one clock is 3:00 pm. The length of the minute hand is 21 units. Find the street traveled by the guideline of the minute hand once the time is 3:30 pm.

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When the minute hand is in ~ 3:30 pm, it covers half of the circle. So, the distance traveled by the minute hand is actually half of the circumference. Street (= pi) (where r is the size of the minute hand). Thus the distance covered = 22/7 × 21 = 22 × 3 = 66 units. Therefore, the distance traveled is 66 units.