Circumference and area of a circle · Usually met around P6
Circumference
Circumference = 3.14 × diameter.
How to do it
Method
Circumference = 3.14 × diameter
Radius 5: 3.14 × 10 = 31.4
Another way
2 × π × radius
2 × 3.14 × 5 = 31.4
In full
The circumference is the distance once round a circle. For every circle, circumference ÷ diameter is the same number, called pi (π), about 3.14 (or 227), so a circumference is always a little more than 3 times the diameter: circumference = π × diameter. First check whether you have the radius or the diameter: a radius of 5 cm is a diameter of 5 × 2 = 10 cm, so the circumference is 3.14 × 10 = 31.4 cm. Another way: circumference = 2 × π × radius, 2 × 3.14 × 5 = 31.4, the same. Check: it should be a little more than 3 times the diameter, 10 × 3 = 30, so 31.4 makes sense.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Find the circumference of this circle. (Take π as 3.14.) The answer is □ cm
Show the answer and working
Answer: 21.98
Circumference = 3.14 × diameter = 3.14 × 7 = 21.98.
Example 2
Take π as 227. What is the circumference of a circle 49 cm across, in cm?
Show the answer and working
Answer: 154 cm
227 × 49 = 22 × 7 = 154: with a diameter in sevens, 227 is handy.
Example 3
A circle of radius 5 cm has a circumference of 15.7 cm. (Take π as 3.14.)
True or false?
Show the answer and working
Answer: False
Circumference = 3.14 × diameter, and the diameter is twice the radius: 3.14 × 5 × 2 = 31.4.
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