Isometric drawing of 3D shapes

Task goals

• Count how many unit cubes make up a solid shown in an isometric drawing, including the cubes that are hidden from the viewer.
• Name the 3D shape shown in an isometric drawing, and state how many faces, edges, and vertices a cube, a triangular prism, or a square-based pyramid has.
• Find the volume of a cube stack drawn in isometric view by counting unit cubes, given that one cube represents 1 cubic centimetre.
• Work out the volume or overall height of a cube arrangement when the edge length of one cube is given, and work backwards from the volume of a single cube to its side length.
• Count the exposed faces of a cube arrangement to give its surface area in unit squares, and, for a solid dipped in paint, count how many of its unit cubes end up with three, one, or no painted faces.
• Split a composite cube solid into layers and find the total number of cubes from the number in each layer, or find the base area in cubes from a given volume and height.
• Justify a cube count in words, explaining why a drawn solid cannot be built from fewer cubes, why a step shape adds a triangular number of cubes per layer, or whether a tower and a cuboid of the same volume are the same solid.
• Design a cube solid to meet given constraints, such as a shape of volume 7 with exactly 3 hidden cubes, or dimensions that give a total of 12 cubes.