Circumference and area of a circle, answers to 3 significant figures or in terms of π, and semicircles and quarter circles.
What you will learn
- Use C = πd and A = πr²
- Give an answer in terms of π
- Find the area and perimeter of semicircles and quarter circles
- Work back from a circumference or area to the radius
Two formulas
The radius r goes from the centre to the edge.
The diameter d goes right across, so d = 2r.
circumference C = πd = 2πr
area A = πr²
- a circle has diameter 10 cm, so r = 5 cm
- C = π × 10 = 31.4159... = 31.4 cm (3 s.f.)
- A = π × 5² = 25π = 78.5398... = 78.5 cm² (3 s.f.)
Keep the full calculator value until the last step, then round.
Working backwards, undo the formula. From an area of 50 cm²: r² = 50 ÷ π = 15.915..., so r = √15.915... = 3.99 cm. From a circumference of 40 cm: r = 40 ÷ (2π) = 6.37 cm (and the diameter is 40 ÷ π = 12.7 cm).
One turn of a wheel moves it forward one circumference. A wheel of diameter 50 cm goes π × 50 = 157.08 cm per turn, so over 30 m = 3000 cm it makes 3000 ÷ 157.08 = 19.1 turns: 19 complete turns (round down). Change both lengths to the same unit first.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Two formulas
- In terms of π
- Parts of a circle
- Try it: Check on the calculator
7 practice questions, marked as you go; about 25 minutes in all.
Key terms
Radius, Diameter, Perimeter
In this unit: Area, perimeter and volume
Perimeter and area of rectangles, triangles, parallelograms, trapeziums and compound shapes, circles, arcs and sectors, and the volume and surface area of prisms, cylinders, pyramids, cones and spheres.