The pattern
Circles and curved boundaries
Find the space inside a circle shape or the distance around its boundary.
A circle carries two different measurements: the space covered inside it, its area, is measured in square centimetres, while the distance around its curved edge, its circumference, is measured in plain centimetres. Both come from the radius, but through different working: area multiplies the radius by itself and by pi, circumference multiplies the diameter by pi. A shape combining straight sides with a curved edge needs each part measured with the right kind.
How to spot it
'Area' asks for square centimetres from the radius. 'Circumference' or 'perimeter' on a curved edge asks for plain centimetres from the diameter instead.
Common mistake
Children give a circumference answer in square units, or find a circle's area without squaring the radius first, mixing up the two kinds of measurement.
14 worked solutions
Standard
- circle area — radius 14 cm A circle has radius 14 cm. Find its area. Use π = 22/7.
- circle area — radius 21 cm A circle has radius 21 cm. Find its area. Use π = 22/7.
- circumference — radius 14 cm A circle has radius 14 cm. Find its circumference. Use π = 22/7.
- circumference — radius 21 cm A circle has radius 21 cm. Find its circumference. Use π = 22/7.
- composite perimeter — radius 14 cm A 42 cm by 28 cm rectangle has a semicircle attached externally to each of its two opposite 28 cm sides. Find the outside perimete…
- composite perimeter — radius 14 cm A 36 cm by 28 cm rectangle has a semicircle attached externally to each of its two opposite 28 cm sides. Find the outside perimete…
- quarter area — radius 14 cm A quarter-circle has radius 14 cm. Find its area. Use π = 22/7.
- quarter area — radius 21 cm A quarter-circle has radius 21 cm. Find its area. Use π = 22/7.
- quarter perimeter — radius 14 cm A quarter-circle has radius 14 cm. Find its full perimeter. Use π = 22/7.
- quarter perimeter — radius 21 cm A quarter-circle has radius 21 cm. Find its full perimeter. Use π = 22/7.
- semicircle area — radius 14 cm A semicircle has radius 14 cm. Find its area. Use π = 22/7.
- semicircle area — radius 21 cm A semicircle has radius 21 cm. Find its area. Use π = 22/7.
- semicircle perimeter — radius 14 cm A semicircle has radius 14 cm. Find its full perimeter. Use π = 22/7.
- semicircle perimeter — radius 21 cm A semicircle has radius 21 cm. Find its full perimeter. Use π = 22/7.
All the problem patterns → · the revision list
The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
A PDF, and a note when new solutions go up.