Use knowledge of calculating volume to solve problems in a range of contexts | Maths

Starter quiz

What is the volume of this cuboid? ______ cm $^3$

'308' ✓
What is the volume of this cuboid? ______ cm $^3$

'324' ✓
Look at this compound rectilinear shape. What is the size of missing side marked a? ______ cm

'7' ✓
Look at this compound rectilinear shape. What is the size of missing side marked b? ______ cm

'7' ✓
Look at this compound rectilinear shape. What is the size of missing side marked b? ______ cm

'11' ✓
Calculate the volume of this compound cuboid. ______ cm $^3$

'68' ✓

Exit quiz

Look at the image of the compound shape. What is the missing length? ______ cm

'5' ✓
Look at the image of the compound shape. What is the missing length? ______ cm

'9' ✓
Look at the image of the compound shape. What is the missing length? ______ cm

'11' ✓
Which of these expressions would result in a volume of 60 cm $^3$ ?

10 × 3 × 2 ✓

10 × 20 × 30

3 × 5 × 4 ✓

1 × 12 × 5 ✓

11 × 5 × 5
Complete the missing dimension to make this correct: 7 cm × ______ cm × 4 cm = 84 cm $^3$

'3' ✓
Andeep has 54 m $^3$ of sand to fill a sandpit. He knows that the sandpit is 3 m deep. What might the width and the length of the sandpit be?

50 and 4

6 and 3 ✓

2 and 9 ✓

3 and 18

Worksheet

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Lesson Details

Key learning points

Missing dimensions can be deduced from other known dimensions.
Where the volume is known, multiplication or division can be used to find an unknown dimension.
Unknown dimension problems can be applied to different contexts.

Common misconception

Pupils cannot visualise how to calculate the unknown dimensions on the compound shape.

Spend time encouraging pupils to note down 'what they know' onto each shape. Allowing pupils to manipulate the shape with concrete apparatus and to run their finger along the edges of the shape will help visualise what is known and unknown.

Keywords

Deduce - If we use existing facts and logic to help find new facts, we can say that we have deduced the new fact.
Dimension - A dimension is the measurement of an edge in one direction. For example: length, width or height of a 3D shape are dimensions.