Part A — Prisms, pyramids & volume
Three-dimensional objects can be visualised, sketched and built. The volume of a rectangular prism is the number of unit cubes that fill it — found by multiplying length × width × height.
Naming & visualising 3D objects
Q1. Name each: (a) 6 square faces (b) 2 triangular faces and 3 rectangular faces (c) a square base and 4 triangular faces meeting at a point.
Q2. How many faces, edges and vertices does a rectangular prism have?
Counting cubes to find volume
Q3. The prism in the picture is 4 long × 2 wide × 2 high. How many unit cubes in the bottom layer? How many layers? Total cubes?
Q4. Find the volume (in cubic units): (a) 3 × 3 × 2 (b) 5 × 2 × 4 (c) 6 × 1 × 3
Describe & test a method
Q5. Write a sequence of steps that works for any rectangular prism to find its volume. Test your steps on a 4 × 3 × 2 prism.
Q6. A box is 10 cm × 5 cm × 4 cm. What is its volume in cubic centimetres?
Construct
Q7. Using the same 12 cubes, list two different rectangular prisms you could build (give the dimensions of each).