A line is drawn that is 5cm long. Applying a scale factor of 2, the line becomes 2 x 5cm = 10cm long.

A rectangle is drawn that is 5cm by 10 cm.

The area of the rectangle is `5 xx 10 = 50 text(cm)^2`.

Applying a linear scale factor of 2, the lengths of each side of the rectangle are doubled. The area of the rectangle becomes `10 xx 20 = 200 text(cm)^2`, which is four times larger.

If a linear scale factor is applied to an area, then the area is increased by the *square* of the scale factor.

A cuboid is drawn that is `2 text(cm) xx 3 text(cm) xx 4 text(cm)`, which is a volume of 24cm^{3}. Applying a linear scale factor of 2, the sides become `4 text(cm) xx 6 text(cm) xx 8 text(cm)`, giving a volume of 192cm^{3}, which is 8 times larger.

If a linear scale factor is applied to a volume, then the volume is increased by the *cube* of the scale factor.

A cuboid has a volume of 22 cm^{3}. A similar cuboid has a length that is 1.5 times the size of the original. What is the volume of the similar cuboid?

Give the answer to 1 decimal place.

The volume of a shape increases by a cube of the scale factor.

The volume of the enlarged cuboid is `22 xx 1.5^2 = 74.25`

To 1 dp this is 74.3cm^{3}

Answer: 74.3 cm^{3}

A rectangle, A, has an area of 100cm^{2}. A similar shape, B, has an area of 200cm^{2}. What is the scale factor to map A onto B? Give the answer correct to 2 decimal places.

A scale factor is squared when relating area

Rectangle A x scale factor^{2} = Rectangle B

Let `f` be the scale factor

Write the relationship | A x `f^2` | `= B` |

Substitute: | 100 x `f^2` | `= 200` |

Divide both sides by 100 | `f^2` | `= 2` |

Square root both sides | `f` | `= 1.412` |

To 2dp | `f` | `= 1.41` |

Answer: 1.41

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