Myths about teaching can hold you back
- Year 10•
- Higher
Using the scale factor for enlarging a volume
I can calculate the scale factor used to enlarge a volume and use it to find missing lengths.
- Year 10•
- Higher
Using the scale factor for enlarging a volume
I can calculate the scale factor used to enlarge a volume and use it to find missing lengths.
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Lesson details
Key learning points
- You can calculate the scale factor from the two volumes.
- Having calculated the scale factor, you can find missing lengths.
Keywords
Similar - Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions.
Invariant - A property of a shape is invariant if that property has not changed after the shape is transformed.
Enlargement - Enlargement is a transformation that causes a change of size.
Scale factor - A scale factor is the multiplier between similar shapes that describes how large one shape is compared to the other.
Volume - Volume is the amount of space occupied by a closed 3D shape.
Common misconception
A linear scale factor can only be found by finding the multiplicative relationship between two corresponding lengths.
A linear scale factor can also be found by cube rooting a volume scale factor, where the volume scale factor is found from the multiplicative relationship between the volumes of two similar 3D shapes.
To help you plan your year 10 maths lesson on: Using the scale factor for enlarging a volume, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: Using the scale factor for enlarging a volume, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
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The assessment exit quiz will test your pupils' understanding of the key learning points.
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Explore more key stage 4 maths lessons from the Similarity unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Prior knowledge starter quiz
6 Questions
Q1.Volume is the amount of occupied by a closed 3D shape.
Q2.A cuboid of dimensions 2 cm by 3 cm by 10 cm is enlarged by a scale factor of 2. Work out the volume of the enlarged cuboid.

Q3.Shape A is a 3D shape. Shape A is enlarged by scale factor 5 to give shape B. What is the volume scale factor from A to B?
Q4.Match each linear scale factor to correct the volume scale factor.
Linear scale factor: $$3$$ -
Volume scale factor: $$27$$
Linear scale factor: $$10$$ -
Volume scale factor: $$1000$$
Linear scale factor: $$2$$ -
Volume scale factor: $$8$$
Linear scale factor: $$6$$ -
Volume scale factor: $$216$$
Linear scale factor: $$9$$ -
Volume scale factor: $$729$$
Q5.Prism S and prism T are similar. What is the scale factor of enlargement from prism S to prism T?

Q6.Prism A and prism B are similar. The end face of prism A has an area of 20 cm². The volume of prism B is cm³.

Assessment exit quiz
6 Questions
Q1.A scale factor is the multiplier between shapes that describes how large one shape is compared to the other.
Q2.The multiplier between corresponding edge lengths on a pair of similar objects is $$k$$. Select the correct statements.
Q3.Shapes X and Y are similar to each other. The volume of shape Y is 729 times larger than the volume of shape X. The linear scale factor from X to Y is .
Q4.Shapes X and Y are similar. The volume of shape Y is 729 times larger than the volume of shape X. The area scale factor from X to Y is .
Q5.Pyramid A and pyramid B are similar. The surface area of pyramid A is 50 cm² and its volume is 120 cm³. The surface area of pyramid B is 200 cm². Calculate the volume of pyramid B.

Q6.Cuboid A and cuboid B are similar. The volume of cuboid B is 405 cm³. The surface area of B is cm².
