Volume of cubes and cuboids

Task goals

• Calculate the volume of a cube or cuboid from a labelled diagram or from given dimensions, using Volume = side cubed for a cube and Volume = length x width x height for a cuboid.
• Find a missing dimension of a cube or cuboid given its volume and its other dimensions.
• Convert a volume between cubic units of measurement (mm cubed, cm cubed, m cubed), and explain why, for example, 1 m cubed equals 1,000,000 cm cubed.
• Solve a real-world volume problem, such as finding the capacity of a container in litres, the volume of a room, or how many unit cubes fit inside a larger box.
• Compare the volumes of two solids, such as a cube and a cuboid, including finding an unknown dimension when two solids have equal volume.
• Write an algebraic expression for the volume of a cube or cuboid using variables for its dimensions, and explain what happens to the volume when its dimensions are scaled by different factors.
• Solve a multi-step real-world volume problem involving a rate, a ratio of dimensions, or rearranging the volume formula to make a dimension the subject.
• Explain why volume is measured in cubic units, and reason about whether a solid's volume can be determined from other given information such as its surface area.