Area of a Circle: Circle is one of the most important geometrical figures. Area of a circle is the space occupied by it. It is calculated as A = πr^2, where r is the radius of the circle. Students must know all the important formulas related to geometry. Questions on area of a circle are asked in great numbers.
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Table of Contents
- Circle and Parts of a Circle
- What is the Area of a Circle?
- Area of Circle- Formulas
- Examples using Area of a Circle Formula
- Area of a Circle- Circulation
- Surface Area of Circle Formula
- Area of Circle Examples
Circle and Parts of a Circle
A circle is a collection of points that are all at the same distance from the circle's centre. A closed geometric shape is a circle. In everyday life, we observe circles such as a wheel, pizza, a circular ground, and so on. The area of the circle is the measurement of the space or region enclosed within 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.
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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 = πr2 or πd2/4 in square units, where π = 22/7 or 3.14, and d is the diameter.
Area of a circle, A = πr2 square units
Circumference / Perimeter = 2πr units
Area of a circle can be calculated by using the formulas:
- Area = π × r2, where 'r' is the radius.
- Area = (π/4) × d2, where 'd' is the diameter.
- Area = C2/4π, where 'C' is the circumference.
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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 = πr2
Put the values,
A = π42
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)×d2
Put the values,
A = (π/4) × 122
A = (π/4) × 144
A = 36π ≈ 113.1
Answer: The area of the circle is 113.1 square units.
Area of a Circle-Calculation
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. | πr2 |
| Area of a circle when the diameter is known. | πd2/4 |
| Area of a circle when the circumference is known. | C2/4π |
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 3-D shape. The surface of a sphere will be spherical in shape but a circle is a simple plane 2-dimensional 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 = πr2 where 'r' is the radius of the circle and the value of π is approximately 3.14 or 22/7.
Area of Circle Examples
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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 = πr2
= 22/7 × 14 × 14
= 22 × 2 × 14
= 616 sq. cm.
Area of the Circle = 616 sq. cm.
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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
Area of a Circle = πr2
πR1R12 : πR2R22 = 4 : 9
Taking square roots of both sides,
R1 : R2 = 2 : 3
Therefore, the ratio of the radii = 2:3
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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 A1 and the area of inner circle be A2
Area of race track = A1 - A2 = πR2 - πr2 = π(632 - 562) = 22/7 × 833 = 2,618 square yards.
Therefore, the area of the race track is 2618 square yards.
How do you find the area of a circle?
The area of a circle is pi times the radius squared (A = π r²). Learn how to use this formula to find the area of a circle when given the diameter.
