3D shapes and surface area
How much card makes a box?
Making boxes
A box is made from a flat net of card. The area of card is the surface area. Designers try to use as little card as possible.
Nets
Count the faces in the net. A cube has 6 square faces. If each is 3 cm × 3 cm, the surface area is 6 × 9 = 54 cm².
Surface area of a cuboid
Top and bottom: 2 × (4 × 3) = 24. Front and back: 2 × (4 × 2) = 16. Sides: 2 × (3 × 2) = 12. Surface area = 24 + 16 + 12 = 52 square units.
Cross-sections
Slice a cylinder: circle. Slice a triangular prism: triangle. Prisms have a constant cross-section.
Regular polyhedra
A regular polyhedron has identical regular faces and the same number meeting at every vertex. There are only 5: tetrahedron, cube, octahedron, dodecahedron and icosahedron. A triangular prism is irregular – its faces are triangles and rectangles.
What I learnt
- I can find surface area from a net.
- I can find the surface area of a cuboid.
- I can describe cross-sections.