Circumference and Area of a Circle – GCSE Maths

Introduction

Circle is very important shape in Geometry. Since it is used in various fields its study is important.
Understanding the concepts of Area and Circumference of a Circle is crucial as it is applied in real life like Construction and even in our daily life measurements. Some of them are –

Circumference of A Circle

The Perimeter of a Circle is Circumference. Basically it is the length of circle’s boundary. It is one-dimensional.
Circumference is used to find the length of a track or wheel’s perimeter like problems in real life.
We can find Circumference of a Circle using its radius with the help of following formula –

Solved Example

Problem: Find the Circumference of the Circle with radius 10 cm.

Solution:

Formula:

Final Answer: 62.8 cm

Area of A Circle

The space enclosed by circumference of Circle is called its Area. It is two-dimensional.
Used to measure the circular object’s area present in real life.
The formula of Area of circle is:

Solved Example

Problem: Find the Area of the Circle with radius 10 cm.

Solution:

Formula:

Final Answer: 314 cm²

Solved Example

Problem: Find out the Circumference and area of the following circles using there diameters

Solution:

First we find the radius of the circle:

(b) Diameter = 4 cm

Radius = 4/2 = 2 cm

(b) Diameter = 6cm

Radius = 6/2 = 3 cm

Final Answer: (a) 12.56 cm² and (b) 28.26 cm²

Solved Example

Problem: Find out the Circumference and area of the circle in terms of π?

Solution:

The diameter of the circle is given using it we can find the circumference:

To find the Area we need to find the diameter first, So –

Diameter = 12 cm,

Radius = 12/2 = 6 cm:

Final Answer: 36π cm²

Solved Example

Problem: Fill in the blanks

Solution:

(1) The Diameter of the Circle is 20cm, So:

(2) The Circumference is given with which we can find the diameter of Circle:

Circumference = 56.52 cm

We can write –

From diameter:

(3) The Radius of the Circle is 5cm, So:

Final Answer:

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