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.
Measuring circumference with help of rope
For a circle with radius ‘r’ and circumference ‘C’:
π = Circumference/Diameter
π = C/2r = C/d
C = 2πr
Example 1 : What is the circumference of a circle of diameter 10 cm (Take π = 3.14)?
Solution: Diameter of the circle (d) = 10 cm
Circumference of circle = πd= 3.14×10cm = 31.4cm
So, the circumference of the circle of diameter 10 cm is 31.4 cm.
Let us understand the different parts of a circle using the following real-life example.
Consider a circular-shaped 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.
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.
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 above 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 circle can be calculated by using the formulas:
The Area of the circle in terms of the diameter is: Area of a Circle = πd2/4. 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.
The area of a circle in terms of the circumference is given by the formula. (Circumference of a Circle)2/4π. 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.
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.
Why is the area of the circle is πr2? To understand this, let's first understand how the formula for the area of a circle is derived.
The circle can be cut into a triangle with the radius being the height of the triangle and the perimeter as its base which is 2πr. We know that the area of the triangle is found by multiplying its base by the height, and then dividing by 2, which is 1/2 x 2πr x r = πr2. Therefore, the area of the circle is πr2, where r, is the radius of the circle and the value of π is 22/7 or 3.14.
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.
Example 3 :
Diameter of a circular garden is 9.8 m. Find its area.
Solution : Diameter, d=9.8m. Therefore, radius r = 9.8 ÷ 2 = 4.9m.
Area of the circle = .
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1. What is the formula for calculating the area of a circle? | ![]() |
2. How do you find the circumference (perimeter) of a circle? | ![]() |
3. What is the relationship between the radius and diameter of a circle? | ![]() |
4. Can I calculate the area of a circle if I only know the circumference? | ![]() |
5. Why is the value of \( \pi \) important in calculating the area and circumference of a circle? | ![]() |