Visualising Solid Shapes

Plane figures such as squares, triangles and circles have only length and breadth, so they are two-dimensional (2-D). Solid shapes such as cubes, cuboids, cylinders, cones, spheres, prisms and pyramids also have height or depth, so they are three-dimensional (3-D). A solid has faces, which are its flat surfaces, edges, where two faces meet, and vertices, the corners where edges meet. A cube has 6 faces, 12 edges and 8 vertices, while a square pyramid has 5 faces, 8 edges and 5 vertices. A net is a 2-D outline that can be folded to make a 3-D shape, and a cube has eleven nets. In this chapter you also learn to draw solids on flat paper. An oblique sketch shows a solid roughly, while an isometric sketch is drawn on isometric dot paper and keeps the true lengths of the edges. You then visualise solids in different ways: by slicing them to see cross-sections, by observing the 2-D shadows they cast in light, and by drawing their front, side and top views.

Detailed Worksheet: Visualising Solid Shapes Section A - Definitions (10 marks) 1. Distinguish between plane figures and solid shapes with two examples of each. (2 marks) 2. Define face, edge and vertex of a solid. (2 marks) 3. What is a net? Give an example. (2 marks) 4. What is the difference between an oblique sketch and an isometric sketch? (2 marks) 5. What is a cross-section of a solid? What cross-section do you get when a loaf of bread is cut vertically? (2 marks) Section B - Calculations and Applications (15 marks) 6. Write the number of faces, edges and vertices of (i) a cube (ii) a cuboid (iii) a triangular prism. (3 marks) 7. Write the number of faces, edges and vertices of (i) a triangular pyramid (ii) a square pyramid. Verify that faces + vertices - edges = 2 for both. (3 marks) 8. A cube of side 3 cm is made by joining small cubes of side 1 cm. (i) How many small cubes are needed? (ii) How many small cubes have 3 faces visible (corners)? (iii) How many are completely hidden inside? (3 marks) 9. Two cubes each of side 2 cm are placed side by side. (i) What are the dimensions of the cuboid formed? (ii) How many faces does it have? (iii) Draw it in words as an oblique sketch. (3 marks) 10. Name the shape of the shadow cast by (i) a ball (ii) a cylindrical can held upright with light from above (iii) the same upright can with light from the side (iv) a cone held upright with light from above (v) a cube (vi) a cone lying on its side with light from above. (3 marks) Section C - Diagrams (10 marks) 11. Draw two different nets of a cube and one net each of a cuboid and a square pyramid. (4 marks) 12. On isometric dot paper, draw an isometric sketch of a cuboid of dimensions 4 cm x 3 cm x 2 cm. (3 marks) 13. Draw the front view, side view and top view of a stack of four cubes arranged in an L shape. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. A cube is cut by a knife in different ways. (i) What cross-section is obtained when cut parallel to a face? (ii) What shape is obtained when cut through a corner, removing one vertex? (iii) What cross-section does a sphere give when cut through any plane? (iv) What cross-section does a cylinder give when cut vertically through its axis? (v) When cut horizontally? (5 marks) 15. A dice has numbers 1 to 6 on its faces such that opposite faces add up to 7. (i) Which number is opposite 2? (ii) Which number is opposite 6? (iii) Draw a net of the dice with correct numbers. (iv) Why can't 1 and 6 be on adjacent faces? (5 marks) 16. Look at a matchbox, a tent, an ice cream cone and a pipe. (i) Name the solid shape of each. (ii) Which of them have curved surfaces? (iii) Which have vertices? (iv) Draw an oblique sketch of the matchbox and the tent. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Use isometric dot paper where asked and label all faces, edges and vertices clearly.