Year 10 - Maths
The effect of enlargement on the volume of a 3D shape
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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 understand the effect of an enlargement on the volume of a 3D shape.
Key Notes
- An enlargement means the object and image are similar.
- All lengths in the object have been multiplied by the scale factor.
- Using index laws, this means the volume has been multiplied by the scale factor cubed.
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
- I will get different linear scale factors if a measure corresponding lengths in cm vs inches.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
An enlargement means the object and image are similar. All lengths in the object have been multiplied by the scale factor.
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: I will get different linear scale factors if a measure corresponding lengths in cm vs inches. Correction: Scale factors do not have dimensions, and aren't linked to specific units. If one length is 23 cm (9 inches), and a corresponding length is 69 cm (27 inches), then the scale factor between them is 3, regardless of whether we measured in cm or inches.
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
- Using the scale factor for enlarging a volume Study Guide
- Using the scale factor for enlarging an area Study Guide
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