GCSE Maths: Best Way To Find The Area Of A Circle
When it comes to calculating the area of a circle there are a few definitions that you need to be aware of as well as two very important formulas.
From the diagram above we have a circle and there are a number of lines that you will see and it is important that you know the names of all these lines.
The black line is the diameter.
The red line is the radius.
The purple line is a chord.
The blue line is a tangent to the circle.
It is important to remember that the diameter is twice the length of the radius.
There are two important formulas that you also need to know.
One is for calculating the circumference of the circle which is essentially the perimeter of the circle. This can be calculated with the following formula:
The other formula that you need to know is how to calculate the area of the circle. This is the space that is inside the shape. The area of a circle is calculated as follows:
It is important to remember that the radius of the circle is being used and not the diameter.
In general we take the value of to be 3.14 unless told otherwise.
Below are some different instances to calculate the area
Different Instances To Calculate The Area Of A Circle
When given the radius:
Here we want to find the area of circle when we are told the radius is 6cm.
When given the diameter:
Remember that if you are given the diameter and in order to find the area you must first halve the radius. So if the diameter is 10cm then the radius will be 5cm.
Area of a Circle - Answers in terms of pi
There will be some instances when a numerical answer is not needed but the answer is required in terms of .
In this instance we are given a circle with diameter 18cm so the radius is 9cm. We can calulate the area as follows:
ππExample 1:
Calculate the area of a circle with circumference 110cm
Solution:
Remember to find the area of a circle we must know the radius.
Here we are told that the circumference and this has the formula C = πd. So we can find “d” as follows:
110 = 3.14 x d
d = 35.03cm and so the radius must be 17.5cm (to 1 dp)
Finding the area we have:
A = 3.14 x 17.5²
A = 962 cm² (nearest whole number)
Example 2:
Find the area of the following quadrant as shown:
Now we only need the area of a quarter of a circle so we must divide the area of the whole circle by 4 and this will give us 38.47 cm²
Example 3:
The small circle is cut away from the larger circle as shown. What area is remaining?
In order to tackle this question you need to determine the area of both circles. You can calculate the area of the large circle and then the area of the small circle and perform a subtraction.
Remaining area = 176.63 – 63.59 = 113.04cm²
Harder Example
When it comes to doing longer questions like this one it is always very important to read the question carefully and to look for any keywords in the question that provide an indication into what calculations you need to do.
One word that sticks out is “area”. So let us start by finding the area of circle A.
For now, we will just leave the answer in terms of and you will see later on why this is a good idea.
What else can be calculated? We are told that the area of circle B is 4 times larger than circle A. This means we can find the area of circle B.
What can be done next? The question is asking for us to write down the ratio of the radius of circle A: the radius of circle B.
The radius of circle A is 12cm. But we don’t know the radius of circle B. What do we know about circle B? We know the area is 576π and from this we can find the radius of circle B.
Hopefully you will see above why leaving the answers to the areas in terms of was handy. Performing the last calculation the terms simply cancelled out which would not have been the case had we had a decimal and we would not get a whole number as the answer.
We are now in a position to complete the question.
Radius Circle A : Radius Circle B = 12 : 24 = 1 : 2
Questions involving the area of a circle can vary quite a great deal in GCSE Maths as we have just seen. The last question required the final answer in terms of a ratio!
Here we have provided a snapshot of what can appear but there is a great deal more of varied questions available. Attend our GCSE Maths Revision Course in London where you will be amongst fellow like minded students who are all looking to achieve the best grades. Classes start at 9:30am and finish at 6:15pm. It is a long day but you do get one hour for lunch and breaks in the morning and afternoon as well.
With area questions especially that of the circle you should try to draw a diagram especially if one is not given to you. These questions can be quite visual and with a sketch in front of you it can help you understand the question better and to form a clearer strategy on how to proceed with the question.
Below are some additional maths questions regarding the circle for you to try with answers at the bottom of the page.
Multiple Choice Questions
What is the area of a circle with radius 4cm?
a. 51.24 cm²
b. 50.24cm²
c. 53.95 cm²
d. 72.22 cm²
What is the area of a circle with radius 6.2cm?
a. 135 cm²
b. 88 cm²
c. 120.70cm²
d. 128.36 cm²
What is the area of a circle with diameter 5.5cm?
a. 24 cm²
b. 32.57 cm²
c. 18 cm²
d. 23.75cm²
What is the area of a circle with diameter 4.9cm
a. 21 cm²
b. 18.85cm²
c. 24.57 cm²
d. 19 cm²
What is the radius of a circle with area 52cm²
a. 4.07cm
b. 3cm
c. 4.52cm
d. 5.63cm
What is the diameter of a circle with area 28cm²
a.6cm
b. 4cm
c. 4.52cm
d. 5.98cm
What is the area of a circle with radius 5cm? (Give answer in terms of )
a. 16 cm²
b. 49 cm²
c. 81 cm²
d. 25 cm²
What is the area of a circle with diameter 12cm? (Give answer in terms of )
a. 16 cm²
b. 36 cm²
c. 100 cm²
d. 144 cm²
What is the area of a semicircle with base 13cm?
a. 66.33 cm²
b. 77.25 cm²
c. 88.59 cm²
d. 43.65 cm²
The circle shown is cut away from the square. What is the remaining area giving your answer to 2 decimal places?
a. 26.02 cm²
b. 27.65 cm²
c. 26.01 cm²
d. 27.56 cm²
Answers:
1 – b; 2 – c; 3 – d; 4 – b; 5 – a; 6 – c; 7 – d; 8 – b; 9 – a; 10 – c
Whatever your goals if you need help getting those top grades then just complete the form and we will be in contact within 24 hours