Stop confusing radius and diameter: Circle geometry - easy as pie part 1
Not that kind of pi - But do you want custard with it?
I was meant to write this before my post on circle theorems, but it’s here now.
In this post I will cover everything you need to know about circle geometry for both gcse maths foundation and higher tier:
Parts of a circle
Area and circumference
How to use pi
Practice questions
Possible exam questions
When you eat pie, you have the crust, the filling, a slice and so on…you will now learn the maths way to say these things:
Circumference: The crust of a pi is called the circumference. This is the complete round edge of the circle.
Radius: The radius of a circle is half of the width of the circle. Its one way to measure the size of a circle or pie.
The radius starts at the center of the circle and goes out towards the edge of the circle.
Diameter: This is the full width of the pie or circle and is another way to measure them. The diameter is a line that goes through the center and touches the edges of the circle on either side of the center.
Circmuference, radius and diameter.
The radius is always half of the diameter.
Sectors and Segments:
A sector is a slice. Its like a triangle where two of the sides are a radius.
A segment is a part of the circle, but not the same shape as a slice. Its side is made up of a chord.
Remember sector is like a slice of pie... a segment is a weird chunk of that pie, cut from a random side of that pie.
Other circle parts you need to memorise:
So what kind of questions do they ask you about circles??
You need to know:
How to calculate the area of a circle
How to work out the length of the circumference or an arc
How to work out the area of a sector
How to work out the area of a segment
You need to memorise all of the circle theorems and how to apply them
This section ranges from levels 4 to 9.
I will show you how to pick easy marks in the exam - grab your favourite snack and/or drink and stay with me.
How to find the area of a circle:
You need to memorise the formula: pi x radius squared
Sometimes the question will provide the diameter, remember to divide that by 2 to find the radius.
Square the radius, then multiply it by pi using your calculator.
How to find the circumference of a circle
Finding the circumference - or outside edge - is really simple.
You multiply the diameter of the circle by pi.
If you only know the radius, then make sure you double the radius length to get the diameter and then multiply by pi.
If you draw a circle and then take a piece of string and wind it around that circle. Then unwind the string and measure its length, that is what you are calculating when you work out the circumference.
What about finding the area and circumference of a sector?
A sector is part of a circle. We call it a slice in normal english.
In the exam you will need to know how to find the area of a sector and also the perimeter of a sector.
You use the same formulas as before, but you need to multiply it by a fraction that represents how much of a circle it is.
In other words, if you have a semi-circle, which is obviously half a circle.
Lets the diameter is 12 like in the example above.
The area of the full circle would be 113.1
So for a semi-circle, its area would be 113.3 x 1/2
If it was a quarter of a circle, we would do 113.2 x 1/4 and so on.
However, what its a weird amount?
Usually on a sector, they will tell you the angle of the slice so you know how much of a circle it is.
How to calculate the area of a sector
How to work out Arc length and perimeter of a sector
The arc is a part of the circumference.
So if you have a sector, the curved edge will be an arc.
Similarly, because its part of the circumference, you can work out the full circumference and then multiply it by a fraction to get the length of the arc:
Tip: If a question asks you to find the exact area, or circumference of arc length, it means you need to leave your answer in terms of pi.
E.g. If a circle has radius 5cm, the exact area would be 25π
You leave your answer like that.
Circle Geometry GCSE Maths Practice Questions
Free Quiz: Circle Area, Circumference, Sector Area & Arc Length
1. What is the area of a circle with a radius of 7 cm? (Use π ≈ 3.14)
