Stage 11 · Shape & space
Circles
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, a circle's area = π × radius × radius, taking π as 3.14. 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; its area is half the circle's. The diameter from the circumference goes back the other way: 31.4 ÷ 3.14 = 10. Or write the formulas C = πd and A = πr² and work in columns — the same answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Radius = ? cm
Take π as 3.14
Show the answer and working
Answer: Radius = 10 cm
Diameter = circumference ÷ 3.14: 62.8 ÷ 3.14 = 20, and the radius is half of it, 20 ÷ 2 = 10, so 10
Example 2
Circumference = ? cm
Take π as 3.14
Show the answer and working
Answer: Circumference = 6.28 cm
Circumference = 3.14 × diameter: the diameter is the radius × 2, 1 × 2 = 2, 3.14 × 2 = 6.28, so 6.28
Example 3
Area of the circle = ? cm²
Take π as 3.14
Show the answer and working
Answer: Area of the circle = 28.26 cm²
A circle's area = 3.14 × radius × radius: the radius is the diameter ÷ 2, 6 ÷ 2 = 3, 3 × 3 = 9, 3.14 × 9 = 28.26, so 28.26
Example 4
Perimeter of the semicircle = ? cm
Take π as 3.14
Show the answer and working
Answer: Perimeter of the semicircle = 20.56 cm
A semicircle's perimeter is half the circumference + the diameter: 3.14 × 8 = 25.12, 25.12 ÷ 2 = 12.56, 12.56 + 8 = 20.56, so 20.56
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