Primary 4 Mathematics · Chapter 13 · Answers and explanations
Lesson 13.1: Recall: Naming Solids (answers)
Section A · Multiple choice 4 marks
1. What is this solid?1 mark
(A) cylinder(B) pyramid(C) cone(D) sphere
Answer: (C) coneIt has a round flat base and comes to a point: a cone.
2. A tin of beans is shaped like which solid?1 mark
(A) cone(B) cuboid(C) sphere(D) cylinder
Answer: (D) cylinderIt has 2 flat circles and 1 curved face: a cylinder.
3. A football is shaped like which solid?1 mark
(A) sphere(B) cone(C) cylinder(D) cube
Answer: (A) sphereA ball is round all over and has no flat face: a sphere.
4. A dice has 6 faces. All are squares of the same size. What solid is it?1 mark
(A) cuboid(B) cube(C) cone(D) cylinder
Answer: (B) cubeAll the faces are equal squares: a cube.
Section B · Write your answer 11 marks
5. Name this solid.1 mark
Answer: cuboidIt has 6 rectangular faces: a cuboid.
6. How many flat faces does a cylinder have?1 mark
Answer: 2The top and the bottom are flat circles. The side is curved.
7. Name two solids that have a curved face.1 mark
Answer: Any two of: cone, cylinder, sphereA cone, a cylinder and a sphere all have a curved face.
8. How many flat faces does a cone have?1 mark
Answer: 1Only the round base is flat.
9. Which solid has no flat face?1 mark
Answer: sphereA sphere is round all over.
10. Name the solid that looks like (a) a ball (b) a tissue box.2 marks
Answer: (a) sphere (b) cuboidA ball is a sphere. A tissue box has 6 rectangular faces, so it is a cuboid.
11. How many flat faces does a cube have? What shape are they?2 marks
Answer: 6 faces; squaresA cube has 6 flat faces. Each face is a square.
12. Name the solid with 1 flat face and 1 curved face. Then name the solid with 2 flat faces and 1 curved face.2 marks
Answer: cone; cylinder1 flat and 1 curved face: cone. 2 flat and 1 curved face: cylinder.
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Primary 4 Mathematics · Chapter 13 · Answers and explanations
Lesson 13.2: Prisms and Pyramids (answers)
Section A · Multiple choice 4 marks
1. Which solid is a prism?1 mark
(A) Solid A(B) Solid B(C) Solid C(D) None of them
Answer: (B) Solid BSolid B has two identical triangles at its ends, so it is a prism.
2. Which solid is a pyramid?1 mark
(A) Solid A(B) Solid B(C) Solid C(D) None of them
Answer: (C) Solid CSolid C has a square base and triangles that meet at the top.
3. The two ends of a triangular prism are shaped like...1 mark
(A) squares(B) triangles(C) rectangles(D) circles
Answer: (B) trianglesThe two identical faces at the ends are triangles.
4. Which solid is NOT a prism?1 mark
(A) cube(B) cuboid(C) cone(D) triangular prism
Answer: (C) coneA cone has no pair of identical faces at its ends.
Section B · Write your answer 11 marks
5. What is the shape of the base of this pyramid?1 mark
Answer: squareThe pyramid sits on a square face.
6. What shape are the slanted faces of this pyramid?1 mark
Answer: trianglesThe slanted faces meet at a point, so they are triangles.
7. Is a cuboid a prism? Write yes or no.1 mark
Answer: YesA cuboid has two identical rectangles at opposite ends.
8. Is this solid a prism or a pyramid?1 mark
Answer: pyramidIt has a pentagon base and triangles that meet at the top.
9. Is this solid a prism or a pyramid?1 mark
Answer: prismIt has two identical pentagons at its ends.
10. Write prism or pyramid for each solid: (a) cube (b) square pyramid.2 marks
Answer: (a) prism (b) pyramidA cube has two identical square ends. A square pyramid has one base and triangles meeting at a vertex.
11. Which of these is not a prism: cuboid, triangular prism, cone, cube? Give a reason.2 marks
Answer: cone; it has no pair of identical faces at opposite endsA prism has two identical faces at opposite ends. A cone does not.
12. Write one way a pyramid is different from a prism.2 marks
Answer: A pyramid has one base and triangular faces that meet at a vertex. A prism has two identical faces at opposite ends.Any correct difference is accepted.
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Primary 4 Mathematics · Chapter 13 · Answers and explanations
Lesson 13.3: Faces, Edges and Vertices (answers)
Section A · Multiple choice 4 marks
1. How many faces does a cube have?1 mark
(A) 6(B) 4(C) 8(D) 12
Answer: (A) 6Top, bottom, front, back, left, right: 6 faces.
2. How many vertices does a square pyramid have?1 mark
(A) 4(B) 5(C) 6(D) 8
Answer: (B) 54 on the base and 1 at the top: 5 vertices.
3. How many edges does a triangular prism have?1 mark
(A) 6(B) 5(C) 9(D) 12
Answer: (C) 93 on each end and 3 joining them: 3 + 3 + 3 = 9 edges.
4. How many faces does a triangular pyramid have?1 mark
(A) 3(B) 5(C) 6(D) 4
Answer: (D) 4The base and 3 triangles: 4 faces.
Section B · Write your answer 11 marks
5. How many edges does a cuboid have?1 mark
Answer: 124 on the top, 4 on the bottom and 4 going up: 12 edges.
6. How many vertices does a triangular prism have?1 mark
Answer: 63 at each end: 6 vertices.
7. How many edges does a square pyramid have?1 mark
Answer: 84 on the base and 4 going up to the top: 8 edges.
8. What are the faces of a cylinder?1 mark
Answer: 2 flat faces and 1 curved faceThe top and bottom are flat circles. The side is curved.
9. How many vertices does a cone have?1 mark
Answer: 1The point at the top is the only vertex.
10. A solid has 5 faces: 1 square and 4 triangles. (a) Name the solid. (b) How many edges does it have?2 marks
Answer: (a) square pyramid (b) 8A square base with 4 triangles is a square pyramid. It has 4 + 4 = 8 edges.
11. Complete: a cube has ___ faces, ___ edges and ___ vertices.2 marks
Answer: 6; 12; 8Count the faces, edges and corners of a cube.
12. A solid has 5 faces and 2 of them are triangles. (a) Name the solid. (b) How many vertices does it have?2 marks
Answer: (a) triangular prism (b) 62 triangles and 3 rectangles make a triangular prism. It has 6 vertices.
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Primary 4 Mathematics · Chapter 13 · Answers and explanations
Lesson 13.4: Drawing on Isometric Grids (answers)
Section A · Multiple choice 4 marks
1. How many units high is this cuboid?1 mark
(A) 3 units(B) 2 units(C) 1 unit(D) 4 units
Answer: (B) 2 unitsCount up a vertical edge: 2 units.
2. How many units long is each side of the base of this pyramid?1 mark
(A) 2 units(B) 4 units(C) 3 units(D) 5 units
Answer: (C) 3 unitsCount along the square base: 3 units.
3. Each edge of this cube is how many units long?1 mark
(A) 2 units(B) 4 units(C) 6 units(D) 3 units
Answer: (D) 3 unitsCount along one edge: 3 units.
4. Which drawing shows a cube?1 mark
(A) Drawing A(B) Drawing B(C) Drawing C(D) None of them
Answer: (B) Drawing BAll the edges of Drawing B are the same length.
Section B · Write your answer 11 marks
5. How many units high is this cuboid?1 mark
Answer: 4 unitsCount up a vertical edge: 4 units.
6. How many units long is each edge of this cube?1 mark
Answer: 2 unitsCount along an edge: 2 units.
7. How many units high is this prism?1 mark
Answer: 2 unitsCount up a vertical edge: 2 units.
8. On an isometric grid we draw only the parts of the solid that we can ___.1 mark
Answer: seeWe draw only the parts that can be seen.
9. How many units long is each side of the base of this pyramid?1 mark
Answer: 3 unitsCount along the square base: 3 units.
10. (a) How many units high is this cuboid? (b) How many units long is its longest base edge?2 marks
Answer: (a) 3 units (b) 4 unitsCount up a vertical edge: 3. Count along the longest edge of the base: 4.
11. A cuboid is 5 units high. A cube with edges of 2 units is placed on top of it. How many units high are they together?2 marks
Answer: 7 units5 + 2 = 7 units.
12. Two cuboids are stacked. One is 3 units high and the other is 2 units high. How many units high is the stack?2 marks
Answer: 5 units3 + 2 = 5 units.
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Primary 4 Mathematics · Chapter 13 · Answers and explanations
Lesson 13.5: Identifying Nets (answers)
Section A · Multiple choice 4 marks
1. Which plan is a net of a cube?1 mark
(A) Net A(B) Net B(C) Net C(D) None of them
Answer: (B) Net BNet B has the right pattern. A is a block and C is a row of 5 squares.
2. Which plan is a net of a prism?1 mark
(A) Net A(B) Net B(C) Net C(D) None of them
Answer: (A) Net ANet A has 3 rectangles and 2 triangles: a triangular prism.
3. Which plan is a net of a pyramid?1 mark
(A) Net A(B) Net B(C) Net C(D) None of them
Answer: (C) Net CNet C has a square and 4 triangles that meet at the top.
4. Two plans are nets of a cube. Which one is NOT?1 mark
(A) Net A(B) Net B(C) Net C(D) None of them
Answer: (B) Net BNet B has two squares on the same side of a row of 4. Two faces overlap.
Section B · Write your answer 11 marks
5. How many squares are there in a net of a cube?1 mark
Answer: 6A cube has 6 faces.
6. This net is made of 6 rectangles. What solid does it make?1 mark
Answer: cuboid6 rectangles fold into a cuboid.
7. This net has 3 rectangles and 2 triangles. What solid does it make?1 mark
Answer: triangular prism3 rectangles and 2 triangles fold into a triangular prism.
8. This net has 1 square and 4 triangles. What solid does it make?1 mark
Answer: square pyramidThe triangles meet at a vertex above the square.
9. A net is made of 4 triangles of the same size. What solid does it make?1 mark
Answer: triangular pyramidA triangular pyramid has 4 triangular faces.
10. Is this plan a net of a cube? Write yes or no and give a reason.2 marks
Answer: No; the row of 5 squares overlaps when foldedFive squares in a row cannot fold without the ends overlapping.
11. How many rectangles and how many triangles are in the net of a triangular prism?2 marks
Answer: 3 rectangles and 2 trianglesCount the faces of a triangular prism: 3 rectangles and 2 triangles.
12. Is this plan a net of a cube? Write yes or no and give a reason.2 marks
Answer: Yes; the squares do not overlap when foldedThe staircase pattern folds into a cube.
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Primary 4 Mathematics · Chapter 13 · Answers and explanations
Lesson 13.6: Word Problems: Nets and Solids (answers)
Section A · Multiple choice 4 marks
1. Each face of a cube-shaped box is a square with sides of 4 cm. What is the total area of cardboard for the box?1 mark
(A) 64 cm²(B) 24 cm²(C) 16 cm²(D) 96 cm²
Answer: (D) 96 cm²One face: 4 × 4 = 16 cm². 6 faces: 6 × 16 = 96 cm².
2. A cuboid box is 5 cm long, 3 cm wide and 2 cm high. What is its total surface area?1 mark
(A) 62 cm²(B) 30 cm²(C) 31 cm²(D) 124 cm²
Answer: (A) 62 cm²2 × (5 × 3) + 2 × (5 × 2) + 2 × (3 × 2) = 30 + 20 + 12 = 62 cm².
3. A cube-shaped box has a total surface area of 54 cm². What is the area of one face?1 mark
(A) 6 cm²(B) 9 cm²(C) 18 cm²(D) 27 cm²
Answer: (B) 9 cm²54 ÷ 6 = 9 cm².
4. Ali has drawn 4 squares of a net of a cube. How many more squares does he need?1 mark
(A) 1(B) 3(C) 2(D) 4
Answer: (C) 26 − 4 = 2 more squares.
Section B · Write your answer 11 marks
5. Each face of a cube box is a square with sides of 10 cm. What is the total area of the 6 faces?1 mark
Answer: 600 cm²One face: 10 × 10 = 100 cm². 6 × 100 = 600 cm².
6. A cuboid box is 8 cm long, 3 cm wide and 2 cm high. What is the total area of its faces?1 mark
Answer: 92 cm²2 × 24 + 2 × 16 + 2 × 6 = 48 + 32 + 12 = 92 cm².
7. The total area of all the faces of a cube is 150 cm². What is the area of one face?1 mark
Answer: 25 cm²150 ÷ 6 = 25 cm².
8. How many faces does the net of a triangular pyramid have?1 mark
Answer: 4A triangular pyramid has 4 triangular faces.
9. Mina has drawn 3 squares of a net of a cube. How many more squares does she need?1 mark
Answer: 36 − 3 = 3.
10. A cuboid box is 10 cm long, 6 cm wide and 4 cm high. How much cardboard is needed to make the box?2 marks
Answer: 248 cm²2 × 60 + 2 × 40 + 2 × 24 = 120 + 80 + 48 = 248 cm².
11. A cube-shaped gift box has sides of 7 cm. How much wrapping paper is needed to cover all its faces?2 marks
Answer: 294 cm²One face: 7 × 7 = 49 cm². 6 × 49 = 294 cm².
12. The total area of all the faces of a cube-shaped box is 216 cm². What is the length of one side?2 marks
Answer: 6 cmOne face: 216 ÷ 6 = 36 cm². 6 × 6 = 36, so the side is 6 cm.
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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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