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Lesson 14 of 16

Volume of prisms

I can use the constant cross-sectional area property of prisms to determine their volume.

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Lesson 14 of 16

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Volume of prisms

I can use the constant cross-sectional area property of prisms to determine their volume.

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Key learning points

The shape and area of the base of a prism can be found.
The area of the cross-section multiplied by the length gives the volume of the prism.
This can be used to find the volume of any prism.
Unknown lengths can be found when the volume of a prism is known.

Keywords

Cross-section - a 2D face made from cutting straight through any plane of a 3D object.
Volume - the amount of space occupied by a closed 3D shape.

Common misconception

Pupils may multiply all lengths on the diagram rather than find the area of the cross-section.

Draw the cross-sectional polygon out, find the area and then multiply by the length of the prism.

Pupils could be challenged to draw a prism with a given volume and then another pupil could check it by calculating the volume.

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Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Prior knowledge starter quiz

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6 Questions

Q1.
The area of a triangle with a base length of 12 cm and a perpendicular height of 7 cm is $$\text{ cm}^2$$.

Correct Answer: 42, forty two

Q2.
Which of these calculations, will correctly work out the area of this composite rectilinear shape?

$$15\times8-2\times7$$

Correct answer: $$6\times7+2\times15$$

$$2\times7+6\times7$$

Correct answer: $$8\times7+2\times8$$

Correct answer: $$15\times8-6\times8$$

Q3.
A prism is a polyhedron with a base that is a polygon and a parallel opposite face that is identical. The edges of the two polygons are joined by parallelograms.

Correct Answer: corresponding

Q4.
Select all the units of area.

Correct answer: $$\text{cm}^2$$

$$\text{cm}$$

$$\text{cm}^3$$

Correct answer: $$\text{feet}^2$$

Correct answer: $$\text{hectare}$$

Q5.
Which of these equations has a solution of $$x=4$$?

Correct answer: $$3x+6=18$$

Correct answer: $$9x=36$$

$$7x+5=19$$

$$12x-19=17$$

Correct answer: $$5x+6=2(x+9)$$

Q6.
Starting with first line, put the lines of working in the correct order to solve an equation.

1 - $$7x+6=20$$

2 - $$7x=14$$

3 - $$x=2$$

Assessment exit quiz

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6 Questions

Q1.
is the amount of space occupied by a closed 3D shape.

Correct Answer: Volume, volume

Q2.
All units for volume are units, such as cm³ or feet³.

Correct Answer: cubed

Q3.
The volume of a cuboid with dimensions 8 cm by 9 cm by 15 cm is $$\text{ cm}^3$$.

Correct Answer: 1080, 1 080

Q4.
Select the triangular prism with the volume of 1800 cm³.

Correct Answer: An image in a quiz

Q5.
An L-shaped prism has a volume of 250 m³. It also has a length of 12.5 m. The area of the 'L-shape' is m².

Correct Answer: 20, twenty, 20m², 20 m²

Volume of prisms

Volume of prisms

These resources were made for remote use during the pandemic, not classroom teaching.

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