Key points
All circle calculations use the constant 蟺 (pi). The circumferenceThe distance around a circle; its perimeter. divided by the diameterThe distance across the circle, circumference to circumference, through its centre. gives 蟺. This works for all circles because they are mathematically similar. The circumference is a length and is measured in units, including centimetres and metres.
Pi is an irrational numberA value that cannot be expressed exactly, such as 鈭2 and 蟺. An approximate value for pi is used in calculations; 3郯142 and 3郯14 are commonly used. A modern calculator uses the surdAn irrational number. This includes the square roots that cannot be written as an exact decimal and special values like 蟺. notation of the symbol 蟺 which can be changed to a decimal approximation using the S
鈬
D key, which gives 3郯141592654The ability to round a number to a number of decimal places or to a number of significant figures means that answers can be written to an agreed degree of accuracy.
Video
Watch the video to learn how circles and circumference play an important role in the work Steph does as a football coach, and why circles play a useful part in sport generally.
Understanding the circle and 蟺 (pi)
To understand the circle, particular vocabulary must be learnt:
- The of a circle is its perimeterThe total distance around a shape..
- An arcPart of the circumference. Named as major for over half of the circumference and minor for less than half of the circumference. is part of the circumference.
- The diameterThe distance across the circle, circumference to circumference, through its centre. is the whole distance across the circle through its centre.
- The radiusThe distance from the centre of the circle to the circumference. is the distance from the circumference to the centre of the circle.
- The radius is half the diameter.
What is 蟺 (Pi)?
- 蟺 (pi)Pi is used to represent the ratio of a circumference of a circle to its diameter, denoted with the Greek symbol 蟺 is the ratio of the circumference of a circle to the length of its diameter.
- For all circles, the circumference divided by the diameter gives 蟺.
- Pi (蟺) is a constant.
- 蟺 is an irrational numberA value that cannot be expressed exactly, such as 鈭2 and 蟺, it cannot be expressed exactly so approximations are used in calculations. 蟺 is rounded most often to 3郯142 or 3郯14. The 蟺 button on a calculator gives greater accuracy.
- When using the 蟺 button the answer may be given in terms of 蟺. The surd display can be changed to a decimal value by pressing the S
鈬
D button. - The final answer is rounded to the degree of accuracy asked for in the question. This may be a specific number of decimal places or significant figures.
Example
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Question
Name the highlighted part of each circle.
A shows the diameter. This is the distance across the circle, through its centre.
B shows an arc. This is part of the circumference. It is a minor arc as it is less than halfway around the circle.
C is a radius. This is the distance from the centre of the circle to the circumference.
D shows the circumference. This is the perimeter of the circle, the distance around the shape.
Calculate the circumference of a circle
To find the of a circle use the given approximation for 蟺 or the 蟺 button on a calculator and either the diameterThe distance across the circle, circumference to circumference, through its centre. or the radiusThe distance from the centre of the circle to the circumference..
- The formula for the circumference when using the diameter is 饾應 = 蟺饾拝
- Substitute the value of the diameter into the formulaA fact, rule, or principle that is expressed in words or in mathematical symbols. Plural: formulae..
- Multiply 蟺 by the diameter of the circle.
- The formula for the circumference when using the radius is 饾應 = 2蟺饾挀
- Substitute the value of the radius into the formula.
- Multiply 2 by 蟺 then multiply by the radius, or multiply 蟺 by double the radius. (Double the radius is the same as the diameter).
- Round the answer to the degree of accuracy asked for in the question. This may involve rounding to a number of decimal places, dp, or rounding to a number of significant figures, sf.
To find the circumference in terms of 蟺.
- When the 蟺 button is used on a calculator the answer is automatically given in terms of 蟺. Working without a calculator, the circumference is the diameter value written before 蟺.
Examples
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Question
What is the circumference of a circle with a radius of 5 cm? Give the answer in terms of 蟺 and to 3 significant figures.
The formula for the circumference of a circle is 饾應 = 2蟺饾挀.
Substitute the value of the radius into the formula and calculate.
2 脳 蟺 脳 5 = 10蟺
2 脳 蟺 脳 5 = 31郯41592654
The circumference of the circle is 10蟺 cm which is31郯4 cm to 3 sf.
Calculate the diameter or radius of a circle, given its circumference
To work out the diameter and the radius of a circle from its circumference.
- Divide the circumference by 蟺. This gives the diameter.
- The radius is half of the diameter.
Examples
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Practise pi and working out circumference
Practise pi and working out the circumference of circles with this quiz. You may need a pen and paper to help you with your answers.
Quiz
Real-life maths
The age of a tree can be found by counting the concentricCircles in a plane that have the same centre rings in the cross-section of the trunk. In practical terms, chopping down a tree is not environmentally sound, so another method has been developed using the circumference of a tree trunk.
Measuring the circumference at a height of 1郯4 m (about 4鈥 6鈥) and dividing by 蟺 gives the diameter of the tree. Multiplying the diameter by the growth factor for the particular species of tree then gives an estimate for the tree鈥檚 age.
Game - Divided Islands
Play the Divided Islands game! gamePlay the Divided Islands game!
Using your maths skills, help to build bridges and bring light back to the islands in this free game from 麻豆官网首页入口 Bitesize.
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