Circles: Circumference & Area
Calculate the circumference and area of circles using the formulae C = πd (or 2πr) and A = πr², and solve problems involving perimeters and areas of composite shapes that include circular parts
What a learner can do afterwards
- Calculate the circumference and area of a circle given its radius or diameter
- Find the perimeter or area of a composite shape made from rectangles and semicircles
- Explain the relationship between π, diameter, and circumference informally
The lesson
You already know the parts of a circle. Now you can use two of them, the radius and the diameter, to measure a circle exactly. The distance around a circle is called its circumference. For any circle, the circumference is always about 3.14 times its diameter. That number is called pi, written as the symbol π. So the formula is C = πd, or if you know the radius instead, C = 2πr, since the diameter is twice the radius.
The space inside a circle is its area. The formula is A = πr², so you square the radius first, then multiply by π. Remember: area always uses the radius, never the diameter directly. If you are only given the diameter, halve it first.
A circular table has a radius of 3 cm. Its area is A = π × 3² = π × 9 ≈ 3.14 × 9 = 28.26 cm². Notice the radius gets squared before you multiply by π.
Composite shapes mix straight edges with circular ones. If you see a rectangle with a semicircle stuck on the end, work out the rectangle part and the semicircle part separately, then add them. A semicircle is exactly half of a full circle, so halve the circumference or area formula for that piece.
Circumference is π times the diameter (or 2πr), and area is π times the radius squared; break composite shapes into circles, semicircles, and straight parts, then add the pieces.
Watch it
Where it sits
This opens up
Nothing builds on it yet.
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.