CIRCLE:
A line forming a closed loop, every point on which is a fixed distance from a center point.
A circle is a plane continuous figure connecting points which are equidistant from a given point, known as the center.
The word circle originates from the Latin word 'circus'. Chariot races, very popular in the Roman era were either circular or oblong and eventually the word was used to describe the shape as well.
Area of a circle - Important terms
In order to find the area of a circle, it is essential that we first understand a few important terms related to circles.
The outermost portion of the circle which separates the interior of the circle from the exterior is known as the circumference.
The center, as already mentioned, is the point inside the circle which is equidistant from all points lying on the circumference.
The distance between any point on the circumference from the center is known as the radius.
A line segment connecting any two points of lying on the circumference on the circle is called a chord.
The longest possible chord of a circle is known as a diameter. The diameter equals twice the radius.
Solving the area of a circle
Consider a circle with center P. Let us denote the radius of the circle by 'r' and the diameter by 'd'. Pi (denoted as π) is a numerical value, which is a crucial number used to calculate various attributes of circular figures. Its value up to 2 decimal points is 3.14. In terms of the radius.
we define the area (A) of the circle as: A = π r²
In terms of the diameter, which is twice the radius, this equation can be re-written as:
A = 0.25 π d²
The area in terms of the circumference (C) of the circle is given as:
A = C²/ 4π
Examples and exercises of area of circle.
Example 1: The radius of a circle is 3 inches. What is the area?
A = π r²
A = ( 3.14 ) ( 3 ) 2
A = (3.14) (9)
A = 28.26 in 2
Answer the following :
1) The diameter of a circle is 8 centimeters. What is the area?
2) The radius of a circle is 5 feet. What is the area?
A line forming a closed loop, every point on which is a fixed distance from a center point.
A circle is a plane continuous figure connecting points which are equidistant from a given point, known as the center.
The word circle originates from the Latin word 'circus'. Chariot races, very popular in the Roman era were either circular or oblong and eventually the word was used to describe the shape as well.
Area of a circle - Important terms
In order to find the area of a circle, it is essential that we first understand a few important terms related to circles.
The outermost portion of the circle which separates the interior of the circle from the exterior is known as the circumference.
The center, as already mentioned, is the point inside the circle which is equidistant from all points lying on the circumference.
The distance between any point on the circumference from the center is known as the radius.
A line segment connecting any two points of lying on the circumference on the circle is called a chord.
The longest possible chord of a circle is known as a diameter. The diameter equals twice the radius.
Solving the area of a circle
Consider a circle with center P. Let us denote the radius of the circle by 'r' and the diameter by 'd'. Pi (denoted as π) is a numerical value, which is a crucial number used to calculate various attributes of circular figures. Its value up to 2 decimal points is 3.14. In terms of the radius.
we define the area (A) of the circle as: A = π r²
In terms of the diameter, which is twice the radius, this equation can be re-written as:
A = 0.25 π d²
The area in terms of the circumference (C) of the circle is given as:
A = C²/ 4π
Examples and exercises of area of circle.
Example 1: The radius of a circle is 3 inches. What is the area?
A = π r²
A = ( 3.14 ) ( 3 ) 2
A = (3.14) (9)
A = 28.26 in 2
Answer the following :
1) The diameter of a circle is 8 centimeters. What is the area?
2) The radius of a circle is 5 feet. What is the area?
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