Volumes of right prisms

Explain cubic units and derive rectangular-prism volume from equal unit-cube layers
Identify a uniform cross-section and distinguish its height from the perpendicular prism length
Calculate rectangular, triangular and supplied-area prism volumes exactly
Use consistent units before multiplying area by length
Calculate and check a missing perpendicular prism length from volume and area

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A solid block is built from equal cubes, each with side length 1 cm. Which unit measures how much three-dimensional space the block occupies?

Year 7, Chapter 4, 3 difficulty levels, No calculatorBuild a worksheet

Common mistakes

Using every number without identifying the cross-section

✕\(\displaystyle Multiply all visible lengths, including a sloping side\)✓\(\displaystyle Find the complete cross-sectional area and multiply it by perpendicular prism length\)

A sloping triangle boundary is not its perpendicular height

Halving twice

✕Find the triangular area, then halve its product with the prism length again✓After finding the triangular area, multiply it by the prism length

The triangular cross-section has already been accounted for

Mixing length units

✕\(\displaystyle Multiply square metres by the centimetre number and report cubic metres\)✓\(\displaystyle Convert the length to metres first\)

The three length directions must use consistent units

Multiplying when a length is missing

✕Multiply volume by area to find the missing length✓Divide volume by area to find the missing length

Division undoes the multiplication in V = AL

Difficulty levels

introCalculate rectangular-prism volumes from whole-number dimensions

standardCalculate triangular or supplied-area volumes and decimal rectangular-prism volumes

challengeUse exact decimal values, match mixed units and recover missing prism lengths

Questions about this topic

Does the cross-section have to be the bottom face?+

No. Choose a uniform cross-section and the perpendicular distance through which it extends. A rectangular prism can be considered in more than one orientation

Does right prism mean the end triangle is right-angled?+

No. Right prism describes the joining length being perpendicular to the end faces. A triangular end may have a perpendicular height inside it

Why are volume units cubed?+

Volume combines three perpendicular length directions. One unit cube is one unit long, wide and high

Why is the missing length not in cubic units?+

Dividing volume by cross-sectional area removes two length factors and leaves one length factor

Can I use a calculator?+

No. This topic is practised without a calculator

Which year level and chapter is this?+

Year 7 Mathematics, chapter 4: Geometry and measurement

In this chapter

Classifying shapes by their properties Angle facts and parallel lines Triangle and polygon angle sums Areas of rectangles, triangles and parallelograms Representing solids with nets and views Volumes of right prisms Radius diameter circumference and pi Model lengths, areas and volumes with ratios Translations, reflections and rotations with coordinates Algorithms for classifying shapes

Count cubes in one layer, then count equal layers

Keep one cross-section fixed as it extends through the prism

Find the rectangular cross-section area before volume

Extend the rectangular end through the stated length

A square cross-section does not force a cube

Halve the triangular cross-section, not the finished result twice

Use the two perpendicular sides of a right-triangular end

Multiply the complete triangular area by prism length

Use an interior triangle height, not a sloping boundary

Keep the triangle height separate from prism length

Use a supplied cross-sectional area without recalculating it

Use the area supplied in square units

Multiply square units by a length unit

Use exact decimal dimensions in the same formulas

Extend an exact decimal rectangular area

Keep the exact product of decimal dimensions

Halve once before multiplying by a decimal length

Use a decimal triangle height in an exact volume

A supplied area can already be a decimal

Use both supplied decimal measurements exactly

Match the length unit to the square-area unit

Convert the prism length after finding square metres

Match metres and centimetres before the final product

Combine the triangle half with a converted prism length

Use metres for both the cross-section and extension

A supplied square-metre area still requires a metre length

Do not change a supplied area while converting only the length

Undo multiplication by the cross-sectional area

Recover a rectangular prism length from its volume

Calculate the end area before dividing

Divide by the triangular area, not the rectangle product

A missing prism length can be an exact decimal

Divide cubic units by the supplied square-unit area

Check the recovered decimal length by multiplication

Find one cross-section, then extend it through the solid

Common mistakes

Difficulty levels

Questions about this topic

In this chapter