- Define and explain Circles and pi in your own words
- Use key terms such as Pi (π) accurately
- Apply what you have learned to new examples and questions
- Avoid the common mistakes learners make with this topic
This lesson focuses on Circles and pi: circumference and area of circles, with pi as the link between diameter and circumference.
Circumference and area of circles, with pi as the link between diameter and circumference.
Key ideas
Circles
Circumference equals pi times diameter (C = πd), and area equals pi times radius squared (A = πr²). Do not mix them up: circumference is a length, area is measured in square units.
Area formulae
Rectangle: base times height. Triangle: half times base times height, using the perpendicular height, not the slant side. Trapezium: half times the sum of the parallel sides times the distance between them.
Key term — Pi (π): The ratio of a circle's circumference to its diameter, approximately 3.14159, which is constant for every circle.
Find the circumference of a circle with diameter 14 cm (use π = 3.14).
C = 3.14 × 14 = 43.96 cm.
Answer: C = 3.14 × 14 = 43.96 cm.
- Confusing radius and diameter in circle formulae A = πr² uses the radius; C = πd uses the diameter. If given the diameter, halve it first for area.
- Forgetting units squared for area Area is measured in square units (cm²); perimeter is a length (cm). Always state the right unit.
Practice
A = 3.14 × 25 = 78.5 cm².
Perimeter = 2(7 + 4) = 22 cm; area = 7 × 4 = 28 cm².
Area = ½ × 10 × 6 = 30 cm².
Area = ½ × (8 + 5) × 4 = ½ × 13 × 4 = 26 cm².
Quick check
Which of these best defines "Pi (π)"?
Two angles on a straight line are 112° and x. Find x.
- Circles and pi: circumference and area of circles, with pi as the link between diameter and circumference.
- Circles: Circumference equals pi times diameter (C = πd), and area equals pi times radius squared (A = πr²).
- Angle: The amount of turn between two lines that meet, measured in degrees.
- Watch out for: confusing radius and diameter in circle formulae