Part A — Counting Cubes & Volume
Volume is the amount of space a solid fills, measured in cubic units. For a rectangular prism, count the unit cubes — or multiply length × width × height. Do not forget the cubes hidden at the back and underneath.
1
Count the unit cubes that build each prism above (remember the hidden cubes at the back).
A: B: C: cubes
2
Prism A measures 3 long, 2 wide and 2 high. Show that length × width × height gives the same count you found in question 1.
3
Find the volume of a box that is 5 cm long, 3 cm wide and 2 cm high.
Volume = cm³
4
A cube has a side length of 4 cm. What is its volume?
Answer:
5
A prism is built from exactly 24 unit cubes. Give two different sets of whole-number dimensions it could have.
6
Reasoning. Prisms A and B above are different shapes but both use 12 cubes. Does the volume of a solid depend on its shape, or only on how many cubes fill it? Explain.
Part B — Nets & Solids
A net is a flat pattern that folds up into a solid. Studying nets helps you count a solid’s faces (flat surfaces), edges (where two faces meet) and vertices (corners).
1
Which solid does each net above fold into?
Net A: Net B:
2
Complete the table for a cube.
| Solid | Faces | Edges | Vertices |
|---|---|---|---|
| Cube | |||
| Square pyramid |
3
How many squares are in the net of a cube? How many of each shape are in the net of a square pyramid?
4
A solid has 2 triangular faces and 3 rectangular faces. Name the solid.
Answer:
5
Reasoning. Sketch one net that folds into a cube and one arrangement of 6 squares that does not. How can you tell the difference?
6
Prove it. For any of these solids, add the faces and vertices then subtract the edges (F + V − E). Do it for the cube and the square pyramid. What do you notice?