Perimeter and Area of Circle Explained with Formula and Concepts

A circle is a two-dimensional shape made up of points that are stretched out from a given point (centre) on the plane by a fixed or constant distance (radius). The fixed point is referred to as the circle's origin or centre, and the fixed distance between each point and the origin is referred to as the radius. Calculating the perimeter and area of a circle is one of the earliest ways to learn how to work with pi. Find out how to calculate these measurements in this article that breaks down the formulas used for calculating these values.

A circle

What is the Perimeter of a Circle?

The boundary or overall arc length of a circle's perimeter is known as its perimeter. A circle's circumference is the term used to describe its edge. Therefore, since the perimeter of a circle provides information on its circumference, the formula is also referred to as the circumference of a circle.

The Perimeter of Circle Formula

The circle's radius acts as one of the three variables in the perimeter of a circle formula, along with two constants.

Perimeter of a circle $=2 \pi r=\pi d$ units

Here,

$r=$ radius of the circle

$d=$ diameter of the circle

Perimeter of Circle Formula

How to Find the Area of the Circle?

The area of a circle is the space occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle.

The circle area formula is $A=\pi r^2$.

To calculate the area of the circle, we must know its radius or its diameter. It is calculated by multiplying $\pi$ by the radius squared: $A=\pi r^2$

Here, r is the radius of the circle.

We can also calculate the area of ​​a circle based on its diameter.

We already know that the radius can be expressed as the diameter divided by two:

$D=2 r$

$r=\dfrac{D}{2}$

If we substitute this expression for the radius in the formula for the area of the circle, we obtain the formula as a function of the diameter:

$A=\pi\left(\dfrac{D}{2}\right)^2$

$A=\pi\left(\dfrac{D^2}{4}\right)$

Where $D$ is the diameter of the circle.

Circle Area Formula

The image below shows the area of the circle formula, with $r$ as the radius and $d$ as the diameter.

Circle Area Formula

Solved Examples

Q 1. What is the area of ​​a circular park with a diameter of 8 feet?

Ans: Given that the diameter of the circular park is 8 feet.

Thus, the radius of the park is half the diameter. That is, the radius is 4 feet. Use the formula for the area of a circle, $A=\pi r^2$, where $r$ is the circle's radius. Substitute 4 for $r$ in the formula.

$A=\pi(4)^2$

$A=\pi(16)$

$A=3.14(16)$

$A=50.24 f t^2$

Therefore, the park's area is $50.24 \mathrm{ft}^2$.

Q 2. What is the perimeter of a circle pizza if the area is $25 \mathrm{~cm}^2$?

Ans: The circle area formula is:

$A=\pi r^2$

We substitute the area for the value of $25 \mathrm{~cm}^2$ that gives us the statement:

$25=\pi r^2$

Then we isolate $r$ and operate to obtain its value:

$r =\sqrt{\dfrac{25}{\pi}}$

$r =\sqrt{7.95}$

$r =2.82 \mathrm{~cm}$

Put the value in the perimeter of the circle formula:

$P=2 \pi r$

We substitute the value of the radius in the circumference of a circle formula:

$P=2 \pi(2.82)$

$P=2(3.14)(2.82)$

$P=17.71 \mathrm{~cm}$

The circle's perimeter is $17.71 \mathrm{~cm}$.

Practice Questions

Q 1: What is the perimeter of a circle knowing its diameter is 2m?

Ans: 6.28 m

Q 2: Find the area of ​​a circle with a radius of 20 cm.

Ans: $1256.63 \mathrm{~cm}^2$

Summary

We discussed here in the article the perimeter and area of a circle. The space a circle takes up on a two-dimensional plane is known as the area of the circle. Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. $A=\pi r^2$, where $r$ is the circle's radius, is the formula for calculating a circle's surface area.

The length of the circle's edge determines its circumference. This implies that a circle's circumference and perimeter are equal. The circle's circumference will equal the length of the rope that precisely encircles its edge.