Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 How many small cubes are in this 2 by 2 by 2 stack?
Show worked solution
4 + 4 = 8 cubes.
2 A solid cube is 4 small cubes along each edge. Write the number in one layer, and the number altogether.
Show worked solution
16 in a layer and 16 × 4 = 64 altogether.
3 How many small cubes are in a solid 3 by 3 by 3 cube?
Show worked solution
27.
Level 2 · Core
4 A solid 3 by 3 by 3 cube is painted all over and split up. How many small cubes have exactly three painted faces?
Show worked solution
A cube has 8 corners, so 8 small cubes have 3 painted faces.
5 In the same painted 3 by 3 by 3 cube, write how many small cubes have exactly one painted face, and how many have none.
Show worked solution
6 with exactly one, and 1 with none. Check: 8 + 12 + 6 + 1 = 27.
6 How many small cubes are hidden inside a solid 4 by 4 by 4 cube, with no face on the surface?
Show worked solution
A 2 by 2 by 2 block: 8.
Level 3 · Challenge
7 A solid 3 by 3 by 3 cube is painted all over and split into 27 small cubes.1 12 small cubes have exactly two painted faces.
2 26 small cubes have at least one painted face.
3 8 small cubes have no painted faces.
Which statements are correct?
2 26 small cubes have at least one painted face.
3 8 small cubes have no painted faces.
Which statements are correct?
Show worked solution
12 edge cubes have exactly two (1 ✓); only the centre is unpainted, so 26 have at least one (2 ✓) and just 1 has none, not 8 (3 ✗). 1 and 2.
8 This stack is made of 6 cubes. Write how many squares are in its front view, and how many are in its top view.
Show worked solution
The front view has 4 squares and the top view has 5.
9 A solid 5 by 5 by 5 cube is painted all over. How many small cubes have no painted faces at all?
Show worked solution
3 × 3 × 3 = 27.