Year 10 - Maths
Using the scale factor for enlarging a volume
Similarity
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit, pupils investigate the effect of an enlargement on the perimeter and area of a 2-D shape and the volume of a 3-D shape.
Lesson Summary
You will learn to calculate the scale factor used to enlarge a volume and use it to find missing lengths.
Key Notes
- You can calculate the scale factor from the two volumes.
- Having calculated the scale factor, you can find missing lengths.
Vocabulary To Learn
- 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 Mistakes To Avoid
- A linear scale factor can only be found by finding the multiplicative relationship between two corresponding lengths.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
You can calculate the scale factor from the two volumes. Having calculated the scale factor, you can find missing lengths.
2. Use this key word in a maths sentence and explain it clearly. 'Similar'
Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: A linear scale factor can only be found by finding the multiplicative relationship between two corresponding lengths. Correction: 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.
More Lessons In This Unit
- Checking and securing understanding of congruent triangles (ASA) Study Guide
- Checking and securing understanding of congruent triangles (RHS) Study Guide
- Checking and securing understanding of congruent triangles (SAS) Study Guide
- Checking and securing understanding of congruent triangles (SSS) Study Guide
- Checking and securing understanding of direct proportion in context Study Guide
- Problem solving with advanced similarity knowledge Study Guide
- Problem solving with similarity Study Guide
- The effect of enlargement on the area of a shape Study Guide
- The effect of enlargement on the perimeter of a shape Study Guide
- The effect of enlargement on the volume of a 3D shape Study Guide
- Using the scale factor for enlarging an area Study Guide
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