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Trace across and around the circle
Task reminder
Find the centre. A radius joins the centre to the circle’s edge.
A radius joins the centre to the circle. A diameter crosses the circle through its centre: it is two radii end to end.
Start at the centre
The dashed diameter passes through the marked centre and reaches both sides of the circle.
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Figure data
This table is included in print while it is open.
| Given | Information |
|---|---|
| Region | Circle |
| Full circle diameter | 14 cm |
| Pi instruction | Use pi = 22/7. Do not round the result. |
The circumference is the distance around the curved boundary. The dashed diameter measures across the circle; it is not another piece of that boundary.
Find the distance around and the space inside
The circle still has diameter 14 cm. Use π = 22/7 for these calculations.
Circumference C measures the boundary; area A measures the enclosed region. Using diameter d and radius r:
Choose a length or an area
The solid outline is the circumference. The enclosed region has an area. The dashed diameter is 14 cm.
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Figure data
This table is included in print while it is open.
| Given | Information |
|---|---|
| Region | Circle |
| Full circle diameter | 14 cm |
| Pi instruction | Use pi = 22/7. Do not round the result. |
Show workingHide answer
The radius is 14/2 = 7 cm. Circumference uses the full diameter:
Area uses the squared radius:
Using the diameter as the radius would double 2π r and make π r² four times as large. Check both the chosen dimension and the units.
Why do the formulas use pi and the squared radius?
For every circle, circumference divided by diameter is the same constant, π. This gives C = π d.
For area, imagine cutting the circle into many thin sectors and alternating them. The shape approaches a rectangle with height r and base half the circumference, π r. Its area approaches π r × r = π r².
Task reminder
Which straight edges must you include with the curve?
Trace the semicircle’s full outline
This semicircle has diameter 14 cm. Use π = 22/7. Its area is half the full circle’s area. Its curved edge is half the full circle’s circumference. Its complete perimeter also includes a straight edge.
Follow both kinds of edge
The solid outline follows the semicircular arc and returns along the diameter.
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Figure data
This table is included in print while it is open.
| Given | Information |
|---|---|
| Region | Semicircle |
| Full circle diameter | 14 cm |
| Pi instruction | Use pi = 22/7. Do not round the result. |
Show workingHide answer
The radius is 7 cm. Area is 1/2 × 22/7 × 7² = 77 cm². The arc is half of the 44 cm circumference, giving 22 cm.
The complete perimeter returns along the 14 cm diameter: 22 + 14 = 36 cm. A fraction of the area needs no extra length; a fraction of the circumference may leave straight boundary edges to include.
Include the quarter circle’s straight edges
Trace the quarter arc, then both radii. The complete boundary contains all three edges.
Check your understanding 1
Area or boundary?
Check your understanding 1
Area or boundary?
A quarter-circle has radius 14 cm. Using π = 22/7, find its area and its complete perimeter. State why the same fraction of a full circle cannot give both answers.
Separate the quarter arc from the two radii
The arc is one quarter of the full circumference. Both straight sides are radii.
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Figure data
This table is included in print while it is open.
| Given | Information |
|---|---|
| Region | Quarter circle |
| Circle radius | 14 cm |
| Pi instruction | Use pi = 22/7. Do not round the result. |
Show answerHide answer
Area is 1/4 × 22/7 × 14² = 154 cm². The curved edge is 22 cm; add two radii of 14 cm to get perimeter 50 cm. A quarter of the full circumference alone omits both straight edges.
Shared edges are not outside edges
Check your understanding 2
Measure the joined region
Check your understanding 2
Measure the joined region
A semicircle is joined outside a rectangle along its full 14 cm side. The rectangle’s other dimension is 10 cm. Use π = 22/7.
Keep the join inside the shape
A is the rectangle and B is the semicircle. Their common 14 cm diameter is dashed; the outside boundary is solid.
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Figure data
This table is included in print while it is open.
| Given | Information |
|---|---|
| A | Rectangle, given figure; side lengths: 14, 10, 14, 10 cm. |
| B | Semicircle, given figure; radius 7 cm. |
| Boundary convention | The shaded region is retained; unshaded regions do not belong to it. Trace every solid boundary, including any enclosed hole edge. Dashed construction guides, if shown, are not extra boundary edges. |
| Pi instruction | Use pi = 22/7. Do not round the result. |
| Drawing convention | Use the given measurements. Do not measure the drawing; its coordinates show the layout only. |
Show workingHide answer
The semicircle’s radius is 7 cm, so its area is 77 cm² and its curved edge is 22 cm. The joined area is 14 × 10 + 77 = 217 cm².
The outside perimeter is 14 + 10 + 10 + 22 = 56 cm. Adding the two complete perimeters would count the internal diameter twice. Tracing the outside directly avoids both copies.
Task reminder
Does the question ask for pi or a rounded number?
Start with the diameter
Keep an exact answer in terms of π when asked. Type pi or π; the units are already beside each response.
Check your understanding 3
Choose the radius before using the area formula
Check your understanding 3
Choose the radius before using the area formula
A circle has diameter 10 m. Give its area and circumference in terms of π. Explain how the diameter enters each formula.
One circle, two different measures
The full diameter is 10 m; it is not the radius.
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Figure data
This table is included in print while it is open.
| Given | Information |
|---|---|
| Region | Circle |
| Full circle diameter | 10 m |
| Pi instruction | Keep pi exact; type pi or π. Do not substitute a decimal approximation. |
Show answerHide answer
The radius is 5 m, so area is π × 5² = 25π m². The circumference is π × 10 = 10π m. Using 100π m² would treat the diameter as the radius. Area requires the squared radius, whereas circumference can use the full diameter directly.
The instruction “use π = 22/7” supplies an approximation for that question. It does not make π exactly equal to 22/7. Here the question asks you to keep π, so a substituted decimal is a different answer form.
Round the final measure
Check your understanding 4
Keep the given radius until the final answer
Check your understanding 4
Keep the given radius until the final answer
A circular patch has radius 1.25 m. Use π = 3.14 and find its area to two decimal places. Explain why you do not first round the radius to 1.3 m.
Keep the radius shown
The known radius is 1.25 m. The figure does not replace it with a rounded length.
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Figure data
This table is included in print while it is open.
| Given | Information |
|---|---|
| Region | Circle |
| Circle radius | 1.25 m |
| Pi instruction | Use pi = 3.14. Round only the final answer to 2 decimal places. |
Show answerHide answer
Keep the known radius of 1.25 m throughout the calculation:
Rounding only this final value gives 4.91 m². Changing the radius first changes the circle being measured. The two-decimal-place instruction applies to the final area asked for.
For a grown-up
Pip’s synthetic voice uses the University of Edinburgh’s Alba speech dataset, via Piper’s Alba voice, under CC BY 4.0. Audio is optional.
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Syllabus and review details
- Primary 6 Mathematics 2026 · 2021-updated-2025-10
- G1 Mathematics 2027 · 2027
- Normal (Technical) Secondary 1 Mathematics 2020 · 2020-reprinted-2023
- G2 Mathematics 2027 · 2027
- Normal (Academic) Secondary 1 Mathematics 2020 · 2020-reprinted-2023
- G3 Mathematics 2027 · 2027
- Express Secondary 1 Mathematics 2020 · 2020-reprinted-2023
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