What are the two circle formulas?

Circumference = 2πr; area = πr².

Why halve the diameter first?

Both formulas use the radius, so halve the diameter before using the area formula.

Why add the diameter to a semicircle?

The perimeter goes right round, and the straight edge of a semicircle is its diameter.

Circumference and Area of a Circle — Practice Paper 1 (10 items with answers)

2026-10-29

Tutor Prep Guide · Primary Maths

A circle needs only two formulas: circumference = 2πr and area = πr². These ten items drill substitution first, then working back to the radius, then semicircles and rings.

Direct answer　Circumference = 2 × π × radius (or π × diameter); area = π × radius × radius. All items take π = 3.14.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10 items
Suggested time	About 20 minutes
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: Primary 6 Maths: Circumference and Area of a Circle — Tutor Lesson Plan
Level	Primary 6

02　Questions (10 items)

FoundationA circle has radius 5 cm. Find its circumference. (Take π = 3.14.)
FoundationA circle has diameter 12 cm. Find its circumference.
FoundationA circle has radius 10 cm. Find its area.
IntermediateA circle has diameter 8 cm. Find its area.
IntermediateA circle has radius 7 cm. Find its circumference and its area.
IntermediateA semicircle has radius 4 cm. Find its perimeter, including the diameter.
ChallengeA circle has circumference 62.8 cm. Find its radius.
ChallengeA circle has area 78.5 cm². Find its radius.
ChallengeA ring has outer radius 6 cm and inner radius 4 cm. Find its area.
Error redoA circle has diameter 10 cm. Find its area. (Common error: using 10 as the radius.)

03　Answers and one-line notes

#	Answer	One-line note
1	31.4 cm	Circumference = 2 × π × radius = 2 × 3.14 × 5 = 31.4 cm.
2	37.68 cm	Circumference = π × diameter = 3.14 × 12 = 37.68 cm.
3	314 cm²	Area = π × radius × radius = 3.14 × 10 × 10 = 314 cm².
4	50.24 cm²	Radius = 8 ÷ 2 = 4 cm, area = 3.14 × 4 × 4 = 50.24 cm².
5	circumference 43.96 cm, area 153.86 cm²	Circumference 2 × 3.14 × 7 = 43.96 cm; area 3.14 × 7 × 7 = 153.86 cm².
6	20.56 cm	The arc is 3.14 × 4 = 12.56 cm; adding the diameter of 8 cm gives 20.56 cm.
7	10 cm	2 × 3.14 × radius = 62.8, so radius = 62.8 ÷ 6.28 = 10 cm.
8	5 cm	3.14 × radius × radius = 78.5, so radius × radius = 25 and radius = 5 cm.
9	62.8 cm²	Area = 3.14 × (36 − 16) = 3.14 × 20 = 62.8 cm².
10	78.5 cm²	The radius is 10 ÷ 2 = 5 cm, so the area is 3.14 × 5 × 5 = 78.5 cm².

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.