Circumference and area of a circle · Usually met around P6
Circumference and area together
Circumference = 3.14 × diameter.
How to do it
Method
Circumference = 3.14 × diameter
Radius 5: diameter 10, 3.14 × 10 = 31.4
Another way
The formula C = πd
3.14 × 5 × 2 = 31.4
In full
Circumference = π × diameter, and a circle's area = π × radius × radius. Use 3.14 for π. First check whether the picture gives the radius or the diameter: diameter = radius × 2. Radius 5 cm: 5 × 2 = 10, so the circumference is 3.14 × 10 = 31.4 cm. The area is 5 × 5 = 25, 3.14 × 25 = 78.5 cm². Quicker: times 10 just moves the decimal point one place right. Split a two-digit number: 3.14 × 12 = 31.4 + 6.28 = 37.68. A semicircle's perimeter is half the circumference plus the diameter, and its area is half the circle's. To get the diameter from the circumference, go backwards: 31.4 ÷ 3.14 = 10. Or write the formulas C = πd and A = πr² and work in columns.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Circumference = ? cm
Take π as 3.14
Show the answer and working
Answer: Circumference = 53.38 cm
Circumference = 3.14 × diameter: 3.14 × 17 = 53.38, so 53.38
Example 2
Radius = ? cm
Take π as 3.14
Show the answer and working
Answer: Radius = 5 cm
Diameter = circumference ÷ 3.14: 31.4 ÷ 3.14 = 10, and the radius is half of it, 10 ÷ 2 = 5, so 5
Example 3
Circumference = ? cm
Take π as 3.14
Show the answer and working
Answer: Circumference = 25.12 cm
Circumference = 3.14 × diameter: the diameter is the radius × 2, 4 × 2 = 8, 3.14 × 8 = 25.12, so 25.12
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