Circumference and area of a circle · Usually met around P6
Area of a circle
3.14 × radius × radius: the radius twice.
How to do it
Method
3.14 × radius × radius: the radius twice
Radius 5: 3.14 × 5 × 5 = 78.5
Another way
Length × width (the almost-rectangle)
3.14 × 5 = 15.7, 15.7 × 5 = 78.5
In full
A circle's area = π × radius × radius, with π as 3.14. Why: cut a circle into many equal slices and lay them top-to-tail as an almost-rectangle, half the circumference (3.14 × radius) long and a radius wide, so the area is 3.14 × radius × radius. Radius 5 cm: 5 × 5 = 25, 3.14 × 25 = 78.5 cm². Given a diameter, halve it first; the radius is multiplied in twice, not doubled. Another way: work out 3.14 × 5 = 15.7 (the almost-rectangle's length) and multiply by the width 5: 15.7 × 5 = 78.5, the same. Check: the area is about 3 times radius × radius, 25 × 3 = 75, so 78.5 makes sense.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Find the area of this circle. (Take π as 3.14.) The answer is □ cm²
Show the answer and working
Answer: 78.5
5 × 5 = 25; 3.14 × 25 = 78.5.
Example 2
Take π as 3.14. What is the area of a circle of radius 4 cm, in cm²?
- A. 12.56
- B. 200.96
- C. 25.12
- D. 50.24
Choose the right answer
Show the answer and working
Answer: D. 50.24
3.14 × 4 × 4 = 50.24.
Example 3
Take π as 3.14. A circle's circumference is 81.64 cm. What is its area, in cm²?
Show the answer and working
Answer: 530.66 cm²
Diameter = 81.64 ÷ 3.14 = 26, so the radius is 13; 3.14 × 13 × 13 = 530.66.
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