How many faces does an open-top box have?

Five: one base and four sides, so add the base once instead of doubling it as for a closed cuboid.

Why does the surface area grow after a cube is cut up?

Cutting creates new faces. The volume stays the same but there are more faces, so the total area increases.

Primary 6 Maths: Surface Area — Practice Paper 4 (10 Questions)

2026-10-29

Paper 4 starts with the three pairs of faces and adds conditions: a cube, an open-top box, a height and an edge recovered from a surface area, then real uses such as painting a wall, cutting a large cube into small ones and wrapping a carton, and finally the error of giving a volume as a surface area.

Quick answer　Ten questions, about 20 minutes. Items 01 to 03 cover a cuboid, a cube and an open-top box; items 04 to 06 recover a height, an edge and a volume, and total the area of several small cubes; items 07 to 09 cover painting costs, the extra area after cutting and a carton; item 10 redoes the volume-for-area error.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10 questions
Suggested time	20 minutes
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: Primary 6 Maths: Surface Area — Tutor Lesson Plan
Level	Primary 6

02　Questions (10 items)

FoundationA cuboid measures 8 cm by 5 cm by 4 cm. What is its surface area?
FoundationA cube has edges of 7 cm. What is its surface area?
FoundationAn open-top box has a 12 cm by 9 cm base and is 5 cm high. What is its surface area?
IntermediateA cuboid has a surface area of 164 cm², a length of 10 cm and a width of 4 cm. What is its height?
IntermediateA cube has a surface area of 96 cm². What is its volume?
IntermediateTwelve small cubes have edges of 3 cm. What is their total surface area?
ChallengeA wall is 6 m long and 3 m high, with 3 m² taken by a door and windows. Two coats cost $8 per square metre. What is the total cost?
ChallengeA cube of edge 6 cm is cut into 8 equal small cubes. By how much does the total surface area increase?
ChallengeA carton measures 25 cm by 18 cm by 12 cm. What is its surface area?
Error redoA cuboid measures 5 cm by 4 cm by 3 cm and a student gives its surface area as 60 cm². What is the correct value and what went wrong?

03　Answers and one-line notes

#	Answer	One-line note
1	184 cm²	Three pairs of faces: 8×5 = 40, 8×4 = 32 and 5×4 = 20 total 92, and 92 × 2 = 184 cm².
2	294 cm²	Each face is 7 × 7 = 49 cm², so six faces give 49 × 6 = 294 cm².
3	318 cm²	With no lid there is one base: 108 + 2×60 + 2×45 = 318 cm².
4	3 cm	The two bases take 80 cm², leaving 84 cm² for the four sides, so 84 ÷ (2 × 14) = 3 cm.
5	64 cm³	One face is 96 ÷ 6 = 16 cm², so the edge is 4 cm and the volume is 64 cm³.
6	648 cm²	One cube is 6 × 9 = 54 cm², so twelve cubes give 54 × 12 = 648 cm².
7	$240	The paintable area is 18 − 3 = 15 m²; two coats cover 30 m², and 30 × 8 = $240.
8	an increase of 216 cm²	The original surface area is 216 cm² and eight 3 cm cubes give 432 cm², an increase of 216 cm².
9	1 932 cm²	The three pairs are 450, 300 and 216, totalling 966; doubling gives 1 932 cm².
10	94 cm²; the volume 5 × 4 × 3 was worked out instead	Surface area adds the six faces: 2 × (20 + 15 + 12) = 94 cm². The 60 is a volume, in cm³.

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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