Printable · GCSE Higher · ages 14-16
Properties of 3D shapes worksheet — GCSE Higher
Fifteen questions on "properties of 3d shapes" — DfE statement G12. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.
Properties of 3D shapes worksheet — GCSE Higher
MathsUKwww.geekhero.co.uk
- 1.A solid has 10 vertices and 15 edges. Using the formula F + V − E = 2, work out how many faces it has.
- 2.A square-based pyramid is cut by a flat plane parallel to its base, partway up between the base and the apex. What shape is the cross-section?
- 3.A cuboid has a length, width and height that are all different from each other. How many planes of symmetry does it have?
- 4.A hexagonal prism lies on a table. A flat cut is made straight across it, at right angles to its length (so the cut is parallel to the two identical end faces). What shape is the cross-section?
- 5.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?
- 6.A solid has 4 triangular faces, 4 vertices and 6 edges. What is the name of this solid?
- 7.A solid has 6 faces and 8 vertices. Using the formula F + V − E = 2, work out how many edges it has.
- 8.A hexagonal prism has 8 faces and 12 vertices. Using F + V − E = 2, work out how many edges it has.
- 9.A packaging designer is told a box has 6 faces, 12 edges and 8 vertices, and every face is a rectangle. To fit exactly onto a shelf, the designer needs to know whether the box must be a cube. Based only on this information, which solid must the box be?
- 10.A cylindrical drum and a cuboid box are being wrapped for a display. A shop assistant wraps only the flat faces of each item, not any curved surface. How many flat faces in total does the assistant wrap across both items?
- 11.A cube has all of its edges the same length. How many planes of symmetry does it have?
- 12.A solid has two parallel, congruent polygon faces joined by flat rectangles, and its cross-section is the same shape all the way along its length. Which solid is it?
- 13.A cone is cut by a flat plane parallel to its circular base, partway up between the base and the apex. What shape is the cross-section?
- 14.A solid has 6 faces: one pentagon and five triangles that all meet at a single point above the pentagon. What is the name of this solid?
- 15.A square-based pyramid has a square base and four identical triangular sloping faces, with its apex directly above the centre of the base. How many planes of symmetry does it have?
Build your own mix at the worksheet builder.