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In order to access this I need to be confident with:
Parts of a circleIrrational numbers
Rounding decimals
Rounding to significant figuresThis topic is relevant for:
Here we will learn about calculating the area of a circle including how to calculate the area of a circle given the radius, how to calculate the area of a circle given the diameter and how to calculate the area of a circle given the circumference.
There are also area of a circle worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if youβre still stuck.
The area of a circle is given by the area of a circle formula which is made by using a specific relationship between the radius of a circle and its area.
Area of a circle formula:
we usually simplify this to
E.g.
What is the area of a circle with radius ?
(pronounced pi) represents the ratio of the circumference of a circle to its diameter.
For all circles if you divide the length of the circumference by the length of the diameter you get the value .
Note: is an irrational number which means it cannot be written as a fraction. It is a non recurring decimal and has an approximate value of
In GCSE you should use the button on your Casio calculator when working with .
To get this you need to press [SHIFT][ ].
Alternatively you can use the value instead.
Sometimes a question may ask you to leave an answer in terms of pi
E.g
(this is an answer in terms of pi)
(this is an answer in terms of pi)
(this is an answer not in terms of pi)
In order to calculate the area of a circle:
Get your free area of a circle worksheet of 20+ questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREEGet your free area of a circle worksheet of 20+ questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREEA circle has a radius of , calculate its area.
Give your answer to .
The radius is given in the question
Radius
2Use the formula to calculate the area of the circle.
3Give your answer clearly with the correct units.
Remember the question asks you to round your answer to β2 decimal placesβ
A circle has a diameter of , calculate its area.
Give your answer to .
Find the radius of the circle.
In this question the question gives you the diameter. You need the radius to find the area of the circle.
Remember the diameter of the circle is twice the radius.
Diameter
Radius
Radius
Use the formula to calculate the area of the circle.
Give your answer clearly with the correct units.
Remember the question asks you to round your answer to β1 decimal placeβ
A circle has a radius of , calculate its area.
Give your answer in terms of .
Find the radius of the circle.
The radius is given in the question
Radius
Use the formula to calculate the area of the circle.
Give your answer clearly with the correct units.
Remember the question asks you to give your answer to βin terms of .
A circle has a diameter of , calculate its area.
Give your answer in terms of
Find the radius of the circle.
In this question the question gives you the diameter. You need the radius to find the area of the circle.
Diameter
Radius
Radius
Use the formula to calculate the area of the circle.
Give your answer clearly with the correct units.
You leave the answer in the form
A circle has a circumference of , calculate its area.
Give your answer to .
Find the radius of the circle.
The question gives you the circumference of the circle. But you need the radius
You know that the circumference of a circle is equal to
This means you can find the radius of the circle from the circumference, see below:
Circumference
Circumference
Divide both sides by
Notice how we leave our answer in terms of
at this stage. This is so you do not cause a rounding error later on in the question.
Use the formula to calculate the area of the circle.
Give your answer clearly with the correct units.
Remember the question asks you to round your answer to β2 decimal placeβ
A semicircle has a diameter of , calculate its area.
Give your answer in terms of
Find the radius of the circle.
In this question the question gives you the diameter. You need the radius to find the area of the circle.
Remember the diameter of the circle is twice the radius.
Diameter
Radius
Radius
Use the formula to calculate the area of the circle.
This represents the area of a whole circle with a diameter of 20m.
A semi circle has half the area of a full circle so you need to divide your answer by two. Remember to keep it in terms of .
Give your answer clearly with the correct units.
You must have the radius to find the area of a circle by using the formula. If a question does not give the radius directly then it must be calculated.
When working with area you must always give the correct units squared
E.g.
etc.
It is important to only round at the end of the question and ensure you are round to what the question specifies.
E.g. to
Sometimes the question may ask you to give the answer in terms of β. This means you do not give the numerical answer that is produced when you multiply it by
E.g.
6 x = 6 (this is an answer in terms of pi)
6 x (this answer is not in terms of pi)
Ensure you know how to correctly use the button on your calculator.
1. A circle has a diameter of . What is the radius of the circle?
The diameter of the circle is twice the size of the radius. Therefore to find the radius you can divide the diameter by
2. Which of these answers is in terms of ?
means lots of
3. A circle has a radius of What is its area to decimal place?
Area of a circle
is equal to
This answer is correctly rounded to decimal place and has the correct units.
4. A circle has a radius of 1cm. What is its area in terms of ?
Area of a circle
is equal to
This answer is correctly given in terms of and has the correct units.
5. A circle has a diameter of What is its area in terms of ?
You must first divide the diameter by to find the radius, divided by is equal to
Therefore the radius is
Area of a circle
is equal to
This answer is correctly given in terms of and has the correct units.
6. A circle has a diameter of What is its area to the nearest whole number?
Area of a circle
is equal to
Which is rounded to the nearest whole number.
1. The radius of a circle is .
Work out the area of the circle.
Give your answer correct to significant figures.
(3 marks)
or seen
(1)
(1)
(1)
2. The radius of a circle is .
Work out the area of the circle.
Give your answer correct to decimal places.
(3 marks)
or seen
(1)
(1)
(1)
3. The diameter of a circle is .
Work out the area of the circle.
Give your answer in terms of .
(3 marks)
(1)
(1)
(1)
4. The diameter of a circle is .
Work out the area of the circle.
Give your answer to 1 decimal place.
(3 marks)
(1)
(1.d.p)
(1)
(1)
5. The circumference of a circle is .
Work out the area of the circle.
Give your answer correct to the nearest integer.
(4 marks)
or seen
(1)
(1)
seen
(1)
(1)
6. A tile is in the shape of a semicircle.
The perimeter of a semi circle is and the length of the arc is .
Work out the total area of the tile.
Give your answer correct to the nearest integer.
(4 marks)
Length of diameter
(1)
or seen
(1)
or seen
(1)
(1)
7. The area of a circle is .
Calculate the radius of the circle.
(3 marks)
(1)
(1)
(1)
Only positive value should be given
You have now learned how to:
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