3D Shapes
Section: Geometry | Syllabus: Cambridge Primary Mathematics (0845)
Compound 3D Shapes
A compound 3D shape is made by joining two or more simple 3D shapes together. Identifying a compound shape means recognising which simple shapes it is built from and how they are joined.
- A compound 3D shape combines two or more basic 3D shapes, joined face-to-face
- Common examples include a cylinder joined to a cuboid (like a can on a box), a pyramid joined to a cuboid (like a tent or house shape), or a cone joined to a cylinder (like an ice cream cone with a scoop)
- To describe a compound shape, name each simple shape it is made from and explain how they are joined
This compound shape is a triangular prism joined face-to-face on top of a cuboid
Worked Example: Describing a Compound Shape
- Question: A solid shape looks like a cylinder standing on top of a cuboid. Describe this compound shape.
- Step 1: Identify the two simple shapes - a cylinder and a cuboid
- Step 2: Identify how they are joined - the circular face of the cylinder sits on top of one face of the cuboid
- Answer: The shape is a cylinder joined face-to-face on top of a cuboid
Common Mistakes
MistakeThinking a compound shape is a single new shape with its own name, rather than a combination of simpler shapes
Fixalways break a compound shape down into the simple 3D shapes it is built from - naming those parts is how you describe it
Nets of 3D Shapes
A net is a 2D shape that can be folded up to make a 3D shape. Every face of the 3D shape appears once in its net, and knowing how the faces connect helps you identify which net matches which shape.
- A cube's net is made of 6 identical squares, arranged so folding along the edges brings all 6 squares together into a cube
- A cuboid's net is made of 3 pairs of matching rectangles - opposite faces of a cuboid are always identical
- A prism's net has 2 identical polygon ends (the cross-section) plus a rectangle for each side face
- A pyramid's net has 1 polygon base plus a triangle for each sloped face, all meeting at a single point (the apex) when folded
Each net shows every face of its 3D shape laid out flat before folding
Worked Example: Checking Whether a Net Folds into a Cube
- Question: A net has 6 squares arranged in a cross shape. Does this fold into a cube?
- Step 1: Count the squares - there are 6, matching the 6 faces of a cube
- Step 2: Check that folding along every edge brings the squares together with no gaps and no overlaps
- Answer: Yes - a cross-shaped arrangement of 6 squares is one of several valid nets of a cube
Common Mistakes
MistakeThinking any arrangement of 6 squares is a valid net for a cube
Fixthe squares must be arranged so that folding closes them up into a cube with no gaps or overlaps - not every 6-square arrangement works
Area of 2D Shapes and Surface Area of 3D Shapes
The surface area of a 3D shape is the total area of all of its flat faces added together. Since a net shows every face of a 3D shape laid out flat, finding the surface area is the same as finding the total area of its net.
- Surface area is the sum of the areas of every face of a 3D shape
- Unfolding a 3D shape into its net turns a 3D surface-area problem into a 2D area problem for each face
- Opposite faces of a cuboid are identical, so their area only needs to be calculated once each and then doubled
Worked Example: Finding the Surface Area of a Cuboid
- Question: A cuboid is 4 cm long, 3 cm wide and 2 cm tall. What is its surface area?
- Step 1: Find the area of one face from each matching pair: 4 × 3 = 12 (top/bottom), 4 × 2 = 8 (front/back), 3 × 2 = 6 (two ends)
- Step 2: Double each area, since there are 2 of each face: 12 × 2 = 24, 8 × 2 = 16, 6 × 2 = 12
- Step 3: Add all the face areas together: 24 + 16 + 12 = 52
- Answer: 52 cm²
Common Mistakes
MistakeForgetting that each face of a cuboid has an identical opposite face
Fixa cuboid has 6 faces in 3 matching pairs - calculate one of each pair, then double it, rather than finding only 3 faces
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