Primary 4 Mathematics · Chapter 13 · Answers and explanations
Chapter 13 Revision Paper: Nets (answers)
Section A · Multiple choice 10 marks
1. Which solid has 2 flat faces and 1 curved face?1 mark
(A) cone(B) sphere(C) cylinder(D) cuboid
Answer: (C) cylinderA cylinder has a flat circle at the top, a flat circle at the bottom and one curved face. A cone has only 1 flat face. A sphere has none.
2. What is the name of this solid?1 mark
(A) triangular pyramid(B) triangular prism(C) cone(D) rectangular pyramid
Answer: (D) rectangular pyramidIt has a rectangle as its base and triangles that meet at the top, so it is a rectangular pyramid.
3. Which solid is a pyramid?1 mark
(A) Solid A(B) Solid B(C) Solid C(D) Solid D
Answer: (A) Solid AA pyramid has one base and triangular faces that meet at a point. Solid A has a triangle base and 3 triangles meeting at the top. The other solids have two flat ends or a curved face.
4. How many faces does this hexagonal prism have?1 mark
(A) 6(B) 8(C) 12(D) 10
Answer: (B) 82 hexagon ends + 6 rectangles = 8 faces. (6 counts only the rectangles, and 12 is the number of vertices.)
5. How many edges does this pentagonal pyramid have?1 mark
(A) 6(B) 15(C) 10(D) 5
Answer: (C) 105 edges round the base and 5 edges going up to the top: 5 + 5 = 10 edges.
6. How many vertices does this pentagonal prism have?1 mark
(A) 7(B) 5(C) 15(D) 10
Answer: (D) 105 vertices on the top pentagon and 5 on the bottom pentagon: 5 + 5 = 10 vertices.
7. This cuboid is drawn on an isometric grid. How many units long is its longest edge?1 mark
(A) 5 units(B) 2 units(C) 3 units(D) 10 units
Answer: (A) 5 unitsCount the dots along the longest edge: 5 units. (3 units is the height and 2 units is the width. 10 units is all three added together.)
8. Which plan is a net of a cube?1 mark
(A) Net A(B) Net B(C) Net C(D) Net D
Answer: (B) Net BNet B folds into a cube: a column of 4 squares with one square on each side. The block of 2 × 3 squares, the row of 5 squares and the row of 4 with two squares on the same side all overlap when folded.
9. Which plan is a net of a square pyramid?1 mark
(A) Net A(B) Net B(C) Net C(D) Net D
Answer: (C) Net CA square pyramid has 1 square and 4 triangles that meet at the top. Net C has 1 square and 4 triangles. The others make a triangular prism, a cuboid and a triangular pyramid.
10. A cuboid box is 9 cm long, 4 cm wide and 3 cm high. What is the total area of all its faces?1 mark
(A) 75 cm²(B) 108 cm²(C) 120 cm²(D) 150 cm²
Answer: (D) 150 cm²There are 3 pairs of faces: 2 × (9 × 4) + 2 × (9 × 3) + 2 × (4 × 3) = 72 + 54 + 24 = 150 cm². (108 is 9 × 4 × 3, which is not the area of the faces.)
Section B · Short answers 4 marks
11. Complete: a triangular pyramid has ___ faces, ___ edges and ___ vertices.1 mark
Answer: 4; 6; 4The base and 3 triangles make 4 faces. 3 edges on the base and 3 going up make 6 edges. 3 vertices on the base and 1 at the top make 4 vertices.
12. This triangular prism is drawn on an isometric grid. How many units high is it?1 mark
Answer: 4 unitsCount up a vertical edge: 4 units.
13. Is this plan a net of a cube? Write yes or no.1 mark
Answer: NoTwo squares are on the same side of the column of 4, so they overlap when folded. It is not a net of a cube.
14. The total area of all the faces of a cube-shaped box is 384 cm². What is the area of one face?1 mark
Answer: 64 cm²A cube has 6 equal faces. 384 ÷ 6 = 64 cm².
Section C · Show your working 16 marks
15. A solid has 7 faces. One face is a hexagon and the other 6 faces are triangles. (a) Name the solid. (b) How many vertices does it have?2 marks
Answer: (a) hexagonal pyramid (b) 7A hexagon base with 6 triangles meeting at the top is a hexagonal pyramid. It has 6 vertices on the base and 1 at the top: 6 + 1 = 7 vertices.
16. Ben has a cube and a triangular pyramid. How many edges do the two solids have altogether?2 marks
Answer: 18A cube has 12 edges. A triangular pyramid has 3 + 3 = 6 edges. 12 + 6 = 18 edges.
17. This cuboid is drawn on an isometric grid. Three of these cuboids are stacked one on top of another. A cube with edges of 2 units is then placed on top. How many units high is the tower?2 marks
Answer: 11 unitsThe cuboid is 3 units high. Three cuboids: 3 × 3 = 9 units. Add the cube: 9 + 2 = 11 units.
18. Five squares of a net of a cube are shaded. One more square must be added to make a net of a cube. Which of the squares P, Q, R or S should be added?2 marks
Answer: ROnly square R makes a net of a cube: the squares then form a staircase of 2 + 2 + 2 squares, and no squares overlap when folded. P, Q and S each make a 2 × 2 block of squares, and a 2 × 2 block cannot fold into a cube.
19. A box without a lid is a cuboid 12 cm long, 7 cm wide and 5 cm high. How much cardboard is needed to make the box?2 marks
Answer: 274 cm²The box has 5 faces: no top. Base: 12 × 7 = 84 cm². Two long sides: 2 × (12 × 5) = 120 cm². Two short sides: 2 × (7 × 5) = 70 cm². 84 + 120 + 70 = 274 cm².
20. Ria has a piece of paper with an area of 500 cm². Can she use it to cover all the faces of a cube-shaped box with edges of 9 cm? If yes, how much paper is left over?2 marks
Answer: Yes; 14 cm² is left overOne face: 9 × 9 = 81 cm². Six faces: 6 × 81 = 486 cm². 486 is less than 500, so she has enough. Paper left: 500 − 486 = 14 cm².
21. Two cubes with edges of 5 cm are glued together face to face to make a cuboid. What is the total area of all the faces of the cuboid?2 marks
Answer: 250 cm²The cuboid is 10 cm long, 5 cm wide and 5 cm high. Faces: 2 × (10 × 5) + 2 × (10 × 5) + 2 × (5 × 5) = 100 + 100 + 50 = 250 cm². (Two separate cubes have 300 cm², but the 2 glued faces are hidden: 300 − 2 × 25 = 250 cm².)
22. The total area of all the faces of a cube is 216 cm². The cube is cut into 2 identical cuboids. What is the total area of all the faces of the 2 cuboids?2 marks
Answer: 288 cm²One face of the cube: 216 ÷ 6 = 36 cm², so each edge is 6 cm. Each cuboid is 6 cm by 6 cm by 3 cm: 2 × (6 × 6) + 4 × (6 × 3) = 72 + 72 = 144 cm². Two cuboids: 2 × 144 = 288 cm². (The cut makes 2 new faces of 36 cm² on each cuboid: 216 + 2 × 36 = 288 cm².)
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