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CIRCUMFERENCE AND AREA OF CIRCLE
Radius
Diameter
Chord
A circle is a simple shape, consisting of those points in a plane that are a given distance from a given point – the centre.
Origin: the center of a circle
Radius: the distance from the center of a circle to any point on it.
Diameter: the longest distance from one end of a circle to the other. The diameter = 2 × radius (d = 2r).
Circumference: the distance around the circle.
Arc: a curved line that is part of the circumference of a circle.
The arc of a circle is measured in degrees or radians – for example: 90° or \ a quarter of the circle, 180° or a half of the circle. The arc is smaller than 360°(or ) because that is the whole circle.
Chord: a line segment within a circle that touches 2 points on the circle.
Sector: is like a slice of pie (a circle wedge).
Tangent: a line perpendicular to the radius that touches ONLY one point on the circle.
Aea of a Circle
The area of a circle is the number of square units inside that circle.
or
where is the area, and is the radius. Let’s look at some examples involving the area of a circle. In each of the three examples below, we will use = 3.14 in our calculations.
Example : The radius of a circle is 3 inches. What is the area of the circle?
Solution:
= 3.14 · (3 in) · (3 in)
= 3.14 · (9 in)
= 28.26 in
Example: The diameter of a circle is 8 centimeters. What is the area of the circle?
8 cm = 2 ·
8 cm ÷ 2 =
= 4 cm
= 3.14 · (4 cm) · (4 cm)
= 50.24 cm
Example : The area of a circle is 78.5 square meters. What is the radius of the circle?
78.5 m = 3.14 · ·
78.5 m ÷ 3.14 · ·
25 m = ·
= 5 m
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 r2
Now, substituting the value:
314.159 = π x r2
314.159 = 3.14 x r2
r2 = 314.159/3.14
r2 = 100.05
r = √100.05
r = 10 cm
Example : What are the circumference and the area of the 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 πr2 cm2
A = (22/7) × 7 × 7
A = 22 × 7
A = 154 cm2
Frequently Asked Questions Using Area of Circle Formula
Example: If the radius of a circle is 15cm. Then find its area.
solution:
Given, radius of circle = 15cm
The area will be;
A = πr2
A = π.152
A = 706.5 sq.cm.
Example: If the diameter of a circle is 10cm. Then find its area.
Solution:
Given, diameter = 10cm
So, radius will be = 10/2 = 5cm
Hence, area A = πr2
A = π.52
A= 78.5 sq.cm
Example: If the circumference of a given circle is 30cm. Then what will be its area?
Solution:
Given, the circumference of a circle = 30cm
We know, from the formula of circumference, C =2πr
So, we can write,
2πr = 30
or r = 30/2π = 15/π
As we found the value of r, now we can find the area;
A = πr2
A = π(15/π)2
On solving we get,
A = 71.65 sq.cm.
Circumference of a Circle
The distance around a rectangle or a square is as you might remember called the perimeter. The distance around a circle on the other hand is called the circumference (c). Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of a circle defines the region occupied by it.
A line that is drawn straight through the midpoint of a circle and that has its end points on the circle border is called the diameter (d)
Half of the diameter, or the distance from the midpoint to the circle border, is called the radius of the circle (r).
The circumference of a circle is found using this formula:
Circumference (or) perimeter of a circle = 2πR or C=π⋅d where,
R is the radius of the circle
π is the mathematical constant with an approximate (up to two decimal points) value of 3.14
Pi (π) is a special mathematical constant; it is the ratio of circumference to diameter of any circle.
where C = π D
C is the circumference of the circle
D is the diameter of the circle
For example: If the radius of the circle is 4cm then find its circumference.
Given: Radius = 4cm
Circumference = 2πr
= 2 x 3.14 x 4
= 25.12 cm
Examples: What is the circumference of the circle with diameter 4 cm?
Solution:
Since the diameter is known to us, we can calculate the radius of the circle,
Therefore, Circumference of the Circle = 2 x 3.14 x 2 = 12.56 cm.
Question 2: Find the radius of the circle having C = 50 cm.
Solution:
Circumference = 50 cm
As per formula, C = 2 π r
This implies, 50 = 2 π r
50/2 = 2 π r/2
25 = π r
or r = 25/π
Therefore, the radius of the circle is 25/π cm.
Quiz
1. What is the area of a circle with radius of 3m?
2. The area of a circle is 78.5 square meters. What is the radius of the circle?
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