The effect of enlargement on the volume of a 3D shape
I can understand the effect of an enlargement on the volume of a 3D shape.
The effect of enlargement on the volume of a 3D shape
I can understand the effect of an enlargement on the volume of a 3D shape.
Lesson details
Key learning points
- 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.
Common misconception
I will get different linear scale factors if a measure corresponding lengths in cm vs inches.
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.
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.
Licence
This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
Video
Loading...
Starter quiz
6 Questions
Exit quiz
6 Questions
Linear scale factor: $$2$$ -
Volume scale factor: $$8$$
Linear scale factor: $$4$$ -
Volume scale factor: $$64$$
Linear scale factor: $$5$$ -
Volume scale factor: $$125$$
Linear scale factor: $$10$$ -
Linear scale factor: $$1000$$
