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Area of a Circle
The area of a circle is the space occupied by the circle in a twodimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr^{2}, where r is the radius of the circle. The unit of area is the square unit, for example, m^{2}, cm^{2}, in^{2}, etc. Area of Circle = πr^{2} or πd^{2}/4 in square units, where (Pi) π = 22/7 or 3.14. Pi (π) is the ratio of circumference to diameter of any circle. It is a special mathematical constant.
The area of a circle formula is useful for measuring the region occupied by a circular field or a plot. Suppose, if you have a circular table, then the area formula will help us to know how much cloth is needed to cover it completely. The area formula will also help us to know the boundary length i.e., the circumference of the circle. Does a circle have volume? No, a circle doesn’t have a volume. A circle is a twodimensional shape, it does not have volume. A circle only has an area and perimeter/circumference. Let us learn in detail about the area of a circle, surface area, and its circumference with examples.
Area of Circle = πr^{2} or πd^{2}/4, square units
where π = 22/7 or 3.14
Circle and Parts of a Circle
A circle is a collection of points that are at a fixed distance from the center of the circle. A circle is a closed geometric shape. We see circles in everyday life such as a wheel, pizzas, a circular ground, etc. The measure of the space or region enclosed inside the circle is known as the area of the circle.
Radius: The distance from the center to a point on the boundary is called the radius of a circle. It is represented by the letter ‘r’ or ‘R’. Radius plays an important role in the formula for the area and circumference of a circle, which we will learn later.
Diameter: A line that passes through the center and its endpoints lie on the circle is called the diameter of a circle. It is represented by the letter ‘d’ or ‘D’.
Diameter formula: The diameter formula of a circle is twice its radius. Diameter = 2 × Radius
d = 2r or D = 2R
If the diameter of a circle is known, its radius can be calculated as:
r = d/2 or R = D/2
Circumference: The circumference of the circle is equal to the length of its boundary. This means that the perimeter of a circle is equal to its circumference. The length of the rope that wraps around the circle’s boundary perfectly will be equal to its circumference. The belowgiven figure helps you visualize the same. The circumference can be measured by using the given formula:
where ‘r’ is the radius of the circle and π is the mathematical constant whose value is approximated to 3.14 or 22/7. The circumference of a circle can be used to find the area of that circle.
For a circle with radius ‘r’ and circumference ‘C’:
 π = Circumference/Diameter
 π = C/2r = C/d
 C = 2πr
Let us understand the different parts of a circle using the following reallife example.
Consider a circularshaped park as shown in the figure below. We can identify the various parts of a circle with the help of the figure and table given below.
In a Circle  In our park  Named by the letter 

Centre  Fountain  F 
Circumference  Boundary  
Chord  Play area entrance  PQ 
Radius  Distance from the fountain to the Entrance gate  FA 
Diameter  Straight Line Distance between Entrance Gate and Exit Gate through the fountain  AFB 
Minor segment  The smaller area of the park, which is shown as the Play area  
Major segment  The bigger area of the park, other than the Play area  
Interior part of the circle  The green area of the whole park  
Exterior part of the circle  The area outside the boundary of the park  
Arc  Any curved part on the circumference. 
What is the Area of Circle?
The area of a circle is the amount of space enclosed within the boundary of a circle. The region within the boundary of the circle is the area occupied by the circle. It may also be referred to as the total number of square units inside that circle.
Area of Circle Formulas
The area of a circle can be calculated in intermediate steps from the diameter, and the circumference of a circle. From the diameter and the circumference, we can find the radius and then find the area of a circle. But these formulae provide the shortest method to find the area of a circle. Suppose a circle has a radius ‘r’ then the area of circle = πr^{2} or πd^{2}/4 in square units, where π = 22/7 or 3.14, and d is the diameter.
Area of a circle, A = πr^{2} square units
Circumference / Perimeter = 2πr units
Area of a circle can be calculated by using the formulas:
 Area = π × r^{2}, where ‘r’ is the radius.
 Area = (π/4) × d^{2}, where ‘d’ is the diameter.
 Area = C^{2}/4π, where ‘C’ is the circumference.
Examples using Area of Circle Formula
Let us consider the following illustrations based on the area of circle formula.
Example 1: If the length of the radius of a circle is 4 units. Calculate its area.
Solution:
Radius(r) = 4 units(given)
Using the formula for the circle’s area,
Area of a Circle = πr^{2}
Put the values,
A = π4^{2}
A =π × 16
A = 16π ≈ 50.27
Answer: The area of the circle is 50.27 squared units.
Example 2: The length of the largest chord of 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 Circle = (π/4)×d^{2}
Put the values,
A = (π/4) × 12^{2}
A = (π/4) × 144
A = 36π ≈ 113.1
Answer: The area of the circle is 113.1 square units.
Area of a Circle Using Diameter
The area of the circle formula in terms of the diameter is: Area of a Circle = πd^{2}/4. Here ‘d’ is the diameter of the circle. The diameter of the circle is twice the radius of the circle. d = 2r. Generally from the diameter, we need to first find the radius of the circle and then find the area of the circle. With this formula, we can directly find the area of the circle, from the measure of the diameter of the circle.
Area of a Circle Using Circumference
The area of a circle formula in terms of the circumference is given by the formula
. There are two simple steps to find the area of a circle from the given circumference of a circle. The circumference of a circle is first used to find the radius of the circle. This radius is further helpful to find the area of a circle. But in this formulae, we will be able to directly find the area of a circle from the circumference of the circle.
Area of a CircleCalculation
The area of the circle can be conveniently calculated either from the radius, diameter, or circumference of the circle. The constant used in the calculation of the area of a circle is pi, and it has a fractional numeric value of 22/7 or a decimal value of 3.14. Any of the values of pi can be used based on the requirement and the need of the equations. The below table shows the list of formulae if we know the radius, the diameter, or the circumference of a circle.
Area of a circle when the radius is known.  πr^{2} 
Area of a circle when the diameter is known.  πd^{2}/4 
Area of a circle when the circumference is known.  C^{2}/4π 
Derivation of Area of a Circle
Why is the area of the circle is πr^{2}? To understand this, let’s first understand how the formula for the area of a circle is derived.
Observe the above figure carefully, if we split up the circle into smaller sections and arrange them systematically it forms a shape of a parallelogram. When the circle is divided into even smaller sectors, it gradually becomes the shape of a rectangle. The more the number of sections it has more it tends to have a shape of a rectangle as shown above.
The area of a rectangle is = length × breadth
The breadth of a rectangle = radius of a circle (r)
When we compare the length of a rectangle and the circumference of a circle we can see that the length is = ½ the circumference of a circle
Area of circle = Area of rectangle formed = ½ (2πr) × r
Therefore, the area of the circle is πr^{2}, where r, is the radius of the circle and the value of π is 22/7 or 3.14.
Surface Area of Circle Formula
The surface area of a circle is the same as the area of a circle. In fact, when we say the area of a circle, we mean nothing but its total surface area. Surface area is the area occupied by the surface of a 3D shape. The surface of a sphere will be spherical in shape but a circle is a simple plane 2dimensional shape.
If the length of the radius or diameter or even the circumference of the circle is given, then we can find out the surface area. It is represented in square units. The surface area of circle formula = πr^{2} where ‘r’ is the radius of the circle and the value of π is approximately 3.14 or 22/7.
RealWorld Example on Area of Circle
Ron and his friends ordered a pizza on Friday night. Each slice was 15 cm in length.
Calculate the area of the pizza that was ordered by Ron. You can assume that the length of the pizza slice is equal to the pizza’s radius.
Solution:
A pizza is circular in shape. So we can use the area of a circle formula to calculate the area of the pizza.
Radius is 15 cm
Area of Circle formula = πr^{2} = 3.14 × 15 × 15 = 706.5
Area of the Pizza = 706.5 sq. cm.
Area of Circle Examples
Example 1: Find the circumference and the area of a circle whose radius is 14 cm.
Solution:
Given: Radius of the circle = 14 cm
Circumference of the Circle = 2πr
= 2 × 22/7 × 14
= 2 × 22 × 2
= 88 cm
Using area of Circle formula = πr^{2}
= 22/7 × 14 × 14
= 22 × 2 × 14
= 616 sq. cm.
Area of the Circle = 616 sq. cm.
Example 2: The ratio of the area of 2 circles is 4:9. With the help of the area of circle formula find the ratio of their radii.
Solution:
Let us assume the following:
The radius of the 1st circle = R1
Area of the 1st circle = A1
The radius of the 2nd circle = R2
Area of the 2nd circle = A2
It is given that A1:A2 = 4:9
Example 3: A race track is in the form of a circular ring. The inner radius of the track is 58 yd and the outer radius is 63 yd. Find the area of the race track.
Solution:
Given: R = 63 yd, r = 56 yd.
Let the area of outer circle be A_{1} and the area of inner circle be A_{2}
Area of race track = A_{1} – A_{2} = πR^{2} – πr^{2} = π(63^{2} – 56^{2}) = 22/7 × 833 = 2,618 square yards.
Therefore, the area of the race track is 2618 square yards.
Example 4: A wire is in the shape of an equilateral triangle. Each side of the triangle measures 7 in. The wire is bent into the shape of a circle. Find the area of the circle that is formed.
Solution:
Perimeter of the Equilateral Triangle: Perimeter of the triangle = 3 × side = 3 × 7 = 21 inches.
Since the perimeter of the equilateral triangle = Circumference of the circle formed.
Thus, the perimeter of the triangle is 21 inches.
Circumference of 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 circle = πr^{2} = 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 length of the minute hand is 21 units. Find the distance traveled by the tip of the minute hand when the time is 3:30 pm.
Solution:
When the minute hand is at 3:30 pm, it covers half of the circle. So, the distance traveled by the minute hand is actually half of the circumference. Distance
(where r is the length of the minute hand). Hence the distance covered = 22/7 × 21 = 22 × 3 = 66 units. Therefore, the distance traveled is 66 units.
FAQs on Area of Circle
How to Calculate the Area of a Circle?
The area of circle is calculated by using the following listed formulas:
 Area = π × r^{2}, where ‘r’ is the radius.
 Area = (π/4) × d^{2}, where ‘d’ is the diameter.
 Area = C^{2}/4π, where ‘C’ is the circumference.
What Is the Area of Circle Formula?
Area of circle formula = π × r^{2}. The area of a circle is π multiplied by the square of the radius. The area of a circle when the radius ‘r’ is given is πr^{2}. The area of a circle when the diameter ‘d’ is known is πd^{2}/4. π is approx 3.14 or 22/7. Area(A) could also be found using the formulas A = (π/4) × d^{2}, where ‘d’ is the radius and A= C^{2}/4π, where ‘C’ is the given circumference.
What Is the Perimeter and Area of a Circle?
The circumference of the circle is equal to the length of its boundary. This means that the perimeter of a circle is equal to its circumference. The area of a circle is πr^{2} and the perimeter (circumference) is 2πr when the radius is ‘r’ units, π is approx 3.14 or 22/7. The circumference and the radius length of a circle are important parameters to find the area of that circle. For a circle with radius ‘r’ and circumference ‘C’:
 π = Circumference ÷ Diameter
 π = C/2r
 Therefore, C = 2πr
Why Is the Area of a Circle Formula is πr^{2}?
A circle can be divided into many small sectors which can then be rearranged accordingly to form a parallelogram. When the circle is divided into even smaller sectors, it gradually becomes the shape of a rectangle. We can clearly see that one of the sides of the rectangle will be the radius and the other will be half the length of the circumference, i.e, π. As we know that the area of a rectangle is its length multiplied by the breadth which is π multiplied to ‘r’. Therefore, the area of the circle is πr^{2}.
What Is the Area of a Circle Formula in Terms of π?
The value of pi (π) is approximately 3.14. Pi is an irrational number. This means that its decimal form neither ends (like 1/5 = 0.2) nor becomes repetitive (like 1/3 = 0.3333…). Pi is 3.141592653589793238… (to only 18 decimal places). Hence the area of a circle formula in terms of pi is given as πr^{2} square units.
How Do You Find the Circumference and Area of a Circle?
The area and circumference of a circle can be calculated using the following formulas. Circumference = 2πr ; Area = πr^{2}. The circumference of the circle can be taken as π times the diameter of the circle. And the area of the circle is π times the square of the radius of the circle.
How to Calculate the Area of a Circle With Diameter?
The diameter of the circle is double the radius of the circle. Hence the area of the circle formula using the diameter is equal to π/4 times the square of the diameter of the circle. The formula for the area of the circle, using the diameter of the circle π/4 × diameter^{2}.
How Do You Find the Area of a Circle Given the Circumference?
The area of a circle can also be found using the circumference of the circle. The radius of the circle can be found from the circumference of the circle and this value can be used to find the area of the circle. Assume that the circumference of the circle is ‘C’. We have C = 2πr, or r = C/2π. Now applying this ‘C’ value in the Area formula we have A = πr^{2} = π × (C/2π)^{2 }= C^{2}/4π.
What Is the Area of Circle With Radius 3 m?
The area of a circle is π multiplied by the square of the radius. The area of a circle(A) when the radius ‘r’ is given is πr^{2}. π is approx 3.14 or 22/7. Therefore, area = 3.14 × 3 × 3 = 28.26 sq. m.
Area of a Circle Calculator
The area of a circle calculator helps you compute the surface of a circle given a diameter or radius. Our tool works both ways – no matter if you’re looking for an area to radius calculator or a radius to the area one, you’ve found the right place ◔
We’ll give you a tour of the most essential pieces of information regarding the area of a circle, its diameter, and its radius. We’ll learn how to find the area of a circle, talk about the area of a circle formula, and discuss the other branches of mathematics that use the very same equation.
How to calculate the area of a circle? Area of a circle formula
So, let’s see how to find the area of a circle. There are several ways to achieve it. Here, we can calculate the area of a circle using a diameter or using a radius.
💡 The diameter is the line that crosses the center of the figure and touches both of its margins. The radius begins at the center of the figure and ends at the figure’s margin.
You can find the diameter of a circle by multiplying the radius of a circle by two:
Diameter = 2 × Radius.
Area of a circle radius. The radius of a circle calculator uses the following area of a circle formula:
Area of a circle = π × r^{2}.
Area of a circle diameter. The diameter of a circle calculator uses the following equation:
Area of a circle = π × (d/2)^{2},
where:
 π is approximately equal to 3.14. It doesn’t matter whether you want to find the area of a circle using diameter or radius – you’ll need to use this constant in almost every case.
Now that you know how to calculate the area of a circle, we encourage you to discover similar topics:
 Circle circumference and perimeter.
 Sector of a circle.
 Pie chart.
 Area of the largest circle in a square.
 A sector of a circle is a section of a circle between two radii. You can think of it as a giant slice of pizza.
 If you want to know how to draw a circle?, the equation for the coordinates and the center of a circle in the coordinate system might come in handy.
How to use the area of a circle calculator? Diameter to area and radius to area.
You can easily calculate everything, the area of a circle, its diameter, and its radius, using our area of a circle calculator in a blink of an eye:

Determine whether your given value is a diameter or a radius using the picture on the right and definitions available in the section above (you can calculate the area of a circle using its diameter as well as radius).

Enter your value into the proper field of the calculator.

It didn’t take long – your results are here! We decided to include the stepbystep solution and all the most important data right below the calculator.
Why do we need the surface area of a circle calculators?
The circle’s area found with both the radius and diameter calculators serves as a base for many other equations – not only in mathematics but also in everyday life! Here are a few examples where knowing how to find the area of a circle might be useful:

We need to know the surface area of a circle in order to calculate a cone’s volume and its surface area 🎉.

Your pizza party wouldn’t be complete without estimating the pizza’s size based on the diameter to area calculator 🍕.

We use calculations similar to this one when obtaining information about a sphere, such as a sphere volume 🌐.

Do you fancy nice dresses? Maybe you love to sew? Discover Omni’s circle skirt calculator! Efficient sewing has never been easier 👗.
Formula
The surface area of a circle is given by the following formula:
A = πr^{2}
where r is the radius of the given circle.
or
A = C^{2}/4π
where C is the circumference of the given circle.
Sample Problems
Question 1. Find the area of a circle given its radius is 8 m.
Solution:
Given: r = 8 m
Since area of a circle = πr^{2}
A = π(8)^{2}
= 64π
= 200.96 m^{2}
Question 2. Find the area of a circle given its circumference is 12 cm.
Solution:
Given: C = 12 cm
Since, A = C^{2}/4π
= 12^{2}/4π
= 11.46 cm^{2}
Question 3. Find the area of a circle given its diameter is 12 cm.
Solution:
Given: D = 12 cm
or, Radius = r = 12/2 = 6 cm
Since A = πr^{2}
= π(6)2
= 113.04 cm^{2}
Question 4. Find the area of a circle given its radius is 9 cm.
Solution:
Given: r = 9 m
Since area of a circle = πr^{2}
A = π(9)^{2}
= 81π
= 254.34 cm^{2}
Question 5. Find the area of a circle given its diameter is 10 cm.
Solution:
Given: D = 10 cm
or, Radius = r = 10/2 = 5 cm
Since A = πr^{2}
= π(5)^{2}
= 78.5 cm^{2}
The Area of a Circle Formula
Examine the “area of a circle” formula: A = π_r_^{2}, where A is the area of the circle and r is the radius of the circle. Archimedes proved this in approximately 260 B.C. using the law of contradiction, and modern mathematics does so more rigorously with integral calculus.
Apply the Surface Area Formula
Now it’s time to use the formula just discussed to calculate the area of a circle with a known radius. Imagine that you’re asked to find the area of a circle with a radius of 2.
The formula for the area of that circle is A = π_r_^{2}.
Substituting the known value of r into the equation gives you A = π(2^{2}) = π(4).
Substituting the accepted value of 3.14 for π, you have A = 4 × 3.14, or approximately 12.57.
Formula for Area From Diameter
You can convert the formula for area of a circle to calculate area using the circle’s diameter, d. Since 2_r_ = d is an unequal equation, both sides of the equal sign must be balanced. If you divide each side by 2, the result will be r = _d/_2. Substituting this into the general formula for area of a circle, you have:
A = π_r_^{2} = π(d/2)^{2} = π(d^{2})/4.
Formula for Area From Circumference
You can also convert the original equation to calculate the area of a circle from its circumference, c. We know that π = c/d; rewriting this in terms of d you have d = c/π.
Substituting this value for d into A = π(d^{2})/4, we have the modified formula:
A = π((c/π)^{2})/4 = c^{2}/(4 × π).
What is a Circle?
A circle closed plane geometric shape. In technical terms, a circle is a locus of a point moving around a fixed point at a fixed distance away from the point. Basically, a circle is a closed curve with its outer line equidistant from the center. The fixed distance from the point is the radius of the circle. In real life, you will get many examples of the circle such as a wheel, pizzas, a circular ground, etc. Now let us learn, what are the terms used in the case of a circle.
Radius
The radius of the circle is the line that joins the center of the circle to the outer boundary. It is usually represented by ‘r’ or ‘R’. In the formula for the area and circumference of a circle, radius plays an important role which you will learn later.
Diameter
The diameter of the circle is the line that divides the circle into two equal parts. In an easy way we can say, it is just the double of the radius of the circle and is represented by ‘d’ or ‘D’. Therefore,
d = 2r or D = 2R
If the diameter of the circle is known to us, we can calculate the radius of the circle, such as;
r = d/2 or R = D/2
Circumference of Circle
A perimeter of closed figures is defined as the length of its boundary. When it comes to circles, the perimeter is given using a different name. It is called the “Circumference” of the circle. This circumference is the length of the boundary of the circle. If we open the circle to form a straight line, then the length of the straight line is the circumference. To define the circumference of the circle, knowledge of a term known as ‘pi’ is required. Consider the circle shown in the fig. 1, with centre at O and radius r.
The perimeter of the circle is equal to the length of its boundary. The length of rope which wraps around its boundary perfectly will be equal to its circumference, which can be measured by using the formula:
Circumference / Perimeter = 2πr units
where r is the radius of the circle.
π, read as ‘pi’ is defined as the ratio of the circumference of a circle to its diameter. This ratio is the same for every circle. Consider a circle with radius ‘r’ and circumference ‘C’. For this circle
 π = Circumference/Diameter
 π = C/2r
 C = 2πr
The same is shown in fig. 2.
What is Area of Circle?
Area of a circle is the region covered or enclosed within its boundary. It is measured in square units.
Any geometrical shape has its own area. This area is the region that occupies the shape in a twodimensional plane. Now we will learn about the area of the circle. So the area covered by one complete cycle of the radius of the circle on a twodimensional plane is the area of that circle. Now how can we calculate the area for any circular object or space? In this case, we use the formula for the circle’s area. Let us discuss the formula now.
Area of a Circle Formula
Let us take a circle with radius r.
In the above figure, we can see a circle, where radius r from the center ‘o’ to the boundary of the circle. Then the area for this circle, A, is equal to the product of pi and square of the radius. It is given by;
Area of a Circle, A = πr^{2} square units 
Here, the value of pi, π = 22/7 or 3.14 and r is the radius.
Derivation of Area of Circle
Area of a circle can be visualized & proved using two methods, namely
 Determining the circle’s area using rectangles
 Determining the circle’s area using triangles
Let us understand both the methods onebyone.
Using Areas of Rectangles
The circle is divided into 16 equal sectors, and the sectors are arranged as shown in fig. 3. The area of the circle will be equal to that of the parallelogramshaped figure formed by the sectors cut out from the circle. Since the sectors have equal area, each sector will have an equal arc length. The red coloured sectors will contribute to half of the circumference, and blue coloured sectors will contribute to the other half. If the number of sectors cut from the circle is increased, the parallelogram will eventually look like a rectangle with length equal to πr and breadth equal to r.
The area of a rectangle (A) will also be the area of a circle. So, we have
 A = π×r×r
 A = πr^{2}
Using Areas of Triangles
Fill the circle with radius r with concentric circles. After cutting the circle along the indicated line in fig. 4 and spreading the lines, the result will be a triangle. The base of the triangle will be equal to the circumference of the circle, and its height will be equal to the radius of the circle.
So, the area of the triangle (A) will be equal to the area of the circle. We have
A = 1/2×base×height
A = 1/2×(2πr)×r
A = πr^{2}
Surface Area of Circle
A circle is nothing but the 2D representation of a sphere. The total area that is taken inside the boundary of the circle is the surface area of the circle. When we say we want the area of the circle, then we mean the surface area of the circle itself. Sometimes, the volume of a circle also defines the area of a circle.
When the length of the radius or diameter or even the circumference of the circle is already given, then we can use the surface formula to find out the surface area. The surface is represented in square units.
The surface area of the circle = A = π x r^{2}
How to Find Area of a Circle?
As we know, the area of circle is equal to pi times square of its radius, i.e. π x r^{2}. To find the area of circle we have to know the radius or diameter of the circle.
For example, if the radius of circle is 7cm, then its area will be:
Area of circle with 7 cm radius = πr^{2} = π(7)^{2} = 22/7 x 7 x 7 = 22 x 7 = 154 sq.cm.
Also, if we know the circumference of the circle, then we can find the area of circle.
How?
Since, the circumference is 2 times of product of pi and radius of circle, such as:
C = 2πr
Therefore, here we can find the value of radius,
r = C/2π
Once, we have evaluated the value of radius, we can easily find the area.
Difference Between Square Area and Circle Area
The area of a circle is estimated to be 80% of area of square, when the diameter of the circle and length of side of the square is the same.
Students can also do an activity by inserting a circular object into a square shape with same diameter and sidelength, respectively.
Solved Examples on Area of a Circle
We have discussed till now the different parameters of the circle such as area, perimeter or circumference, radius and diameter. Let us solve some problems based on these formulas to understand the concept of area and perimeter in a better way.
Example 1:
What is the radius of the circle whose surface area is 314.159 sq.cm?
Solution:
By the formula of the surface area of the circle, we know;
A = π x r^{2}
Now, substituting the value:
314.159 = π x r^{2}
314.159 = 3.14 x r^{2}
r^{2} = 314.159/3.14
r^{2} = 100.05
r = √100.05
r = 10 cm
Example 2:
Find the circumference and the area of circle if the radius is 7 cm.
Solution:
Given: Radius, r = 7 cm
We know that the circumference/ perimeter of the circle is 2πr cm.
Now, substitute the radius value, we get
C = 2 × (22/7)× 7
C = 2×22
C = 44 cm
Thus, the circumference of the circle is 44 cm.
Now, the area of the circle is πr^{2 }cm^{2}
A = (22/7) × 7 × 7
A = 22 × 7
A = 154 cm^{2 }
Example 3:
If the longest chord of a circle is 12 cm, then find the area of circle.
Solution:
Given that the longest chord of a circle is 12 cm.
We know that the longest chord of a circle is the diameter.
Hence, d = 12 cm.
So, r = d/2 = 12/2 = 6 cm.
The formula to calculate the area of circle is given by,
A = πr^{2 }square units.
Now, substitute r = 6 cm in the formula, we get
A = (22/7)×6×6 cm^{2}
A = (22/7)×36 cm^{2}
A = 792/7 cm^{2}
A = 113.14 cm^{2 }(Rouned to 2 decimal places)
Therefore the area of circle is 113.14 cm^{2}.
Frequently Asked Questions on Area of Circle
What is meant by area of circle?
How to calculate the area of a circle?
Area = π x r^{2}, in terms of radius ‘r’.
Area = (π/4) x d^{2}, in terms of diameter, ‘d’.
Area = C^{2}/4π, in terms of circumference, ‘C’.
What is the perimeter of circle?
What is the area of a circle with radius 3 cm, in terms of π?
We know that the area of circle is πr^{2 }square units
Hence, A = π x 3^{2} = 9π cm^{2}.
Find the circumference of circle in terms of π, whose radius is 14 cm.
Hence, C = 2π(14) = 28π cm.
Find the radius of the circle, if its area is 340 square centimeters.
We know that, Area of a circle = πr^{2} square units
Hence, 340 =3.14 r^{2}
Hence, r^{2} = 340/3.14
r^{2} = 108.28
Hence, r = 10.4 cm.
Hence, radius of a circle = 10.4 cm
Determine the area of the circle in terms of pi, if radius = 6 cm.
We know that, Area = πr^{2}
A = π(6)^{2}
A = 36π
Hence, the area of a circle is 36π, if the radius is 6 cm.
Find the area of a circle, if its circumference is 128 inches.
The area of a circle is 1303.8 square inches if its circumference is 128 inches.
Surface Area of Circle Formula
Solved example
Question: What is the radius of the circle whose surface area is 314.159
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