Volume of prisms

The Maths Habit

1 How many squares are shaded?

15

2 Work out the area of the rectangle.

6 cm4 cm
24 cm2

3 What is 8 × 5?

40

Both shapes are made of cubes. Which shape has more cubes, A or B?

A
B

B has 27 cubes. A has 24 cubes.

Volume
The space inside a 3D shape.
Cubic centimetre
The space inside a cube with sides of 1 cm. We write cm³.
Prism
A 3D shape that is the same all the way through.
Cross-section
The face you see when you slice through a prism. It is shaded.

3 cm2 cm4 cm
  1. Find the area of the cross-section.Width × height. It is one layer of cubes.
  2. Multiply by the length.One layer for every cm of length.
  3. Write the units.Volume is in cubic units: cm³.
Cross-sectionwidth×height=cm²
Volume×length=cm³

Work out the volume.

4 cm3 cm2 cm
Cross-section4×3=12cm²
Volume12×2=24cm³

Work out the volume.

2 cm2 cm5 cm
Cross-section2×2=4cm²
Volume4×5=20cm³

Work out the volume.

4 cm3 cm2 cm
Cross-section4×3=12cm²
Volume12×2=24cm³

Work out the volume.

3 cm2 cm3 cm
widthheightlengthCross-section the pink faceVolume cross-section × length
Cross-section3×2=6cm²
Volume6×3=18cm³

Work out the volume.

4 cm3 cm2 cm
Cross-section4×3=12cm²
Volume12×2=24cm³

Work out the volume.

5 cm2 cm3 cm
widthheightlengthCross-section the pink faceVolume cross-section × length
Cross-section5×2=10cm²
Volume10×3=30cm³

Work out the volume.

4 cm3 cm2 cm
Cross-section4×3=12cm²
Volume12×2=24cm³

Work out the volume.

4 cm2 cm4 cm
widthheightlengthCross-section the pink faceVolume cross-section × length
Cross-section4×2=8cm²
Volume8×4=32cm³

Work out the volume of each cuboid.

13 cm3 cm4 cm
Cross-section3×3=9cm²
Volume9×4=36cm³
22 cm4 cm5 cm
Cross-section2×4=8cm²
Volume8×5=40cm³
35 m2 m2 m
Cross-section5×2=10m²
Volume10×2=20m³
widthheightlengthCross-section the pink faceVolume cross-section × length

Which face is the cross-section?

ACBB

Which face is the cross-section?

ABCC

length9 cm²
  1. The area of the cross-section is written on it.Copy it into the frame.
  2. Multiply by the length.The same frame as a cuboid.
  3. Write the units.cm³

Work out the volume.

5 cm8 cm²
Cross-section8cm²
Volume8×5=40cm³

Work out the volume.

4 cm7 cm²
Cross-section7cm²
Volume7×4=28cm³

Work out the volume.

5 cm8 cm²
Cross-section8cm²
Volume8×5=40cm³

Work out the volume.

3 cm6 cm²
widthheightlengthCross-section the pink faceVolume cross-section × length
Cross-section6cm²
Volume6×3=18cm³

Work out the volume.

5 cm8 cm²
Cross-section8cm²
Volume8×5=40cm³

Work out the volume.

4 cm9 cm²
widthheightlengthCross-section the pink faceVolume cross-section × length
Cross-section9cm²
Volume9×4=36cm³

Work out the volume.

5 cm8 cm²
Cross-section8cm²
Volume8×5=40cm³

Work out the volume.

5 cm2 cm7 cm
widthheightlengthCross-section the pink faceVolume cross-section × length
Cross-section5×2=10cm²
Volume10×7=70cm³

Work out the volume of each prism.

14 cm10 cm²
Cross-section10cm²
Volume10×4=40cm³
23 cm2 cm8 cm
Cross-section3×2=6cm²
Volume6×8=48cm³
36 m5 m²
Cross-section5m²
Volume5×6=30m³
widthheightlengthCross-section the pink faceVolume cross-section × length

Is the volume right? Thumbs up or thumbs down.

A3 cm2 cm5 cmVolume = 10 cm3Wrong: 30 cm3
B4 cm6 cm²Volume = 24 cm3Right
C4 cm2 cm3 cmVolume = 24 cm3Right
D3 cm5 cm²Volume = 8 cm3Wrong: 15 cm3

Volume of prisms worksheet, page 1

Volume of prisms worksheet, page 2

Answer sheet

  1. A triangular prism is 5 cm long. Its cross-section is a triangle with a base of 6 cm and a height of 4 cm. Work out its volume.

    60 cm3

  2. A cuboid has a volume of 48 cm³. The area of its cross-section is 8 cm². How long is the cuboid?

    6 cm

  3. A prism has a cross-section of 4.5 cm². It is 2 cm long. Work out its volume.

    9 cm3

  1. Work out the volume of the cuboid. Cross‑section5×2=10cm²

    Volume = 90 cm3
    5 cm2 cm9 cm

  2. Work out the volume of the prism. Volume7×5=35cm³

    35 cm3
    5 cm7 cm²

  3. Work out the volume of the cuboid.

    56 cm3
    2 cm4 cm7 cm
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