  # Volume Scale Factor - Simple Problems

In this worksheet students will be able to find volume of similar shapes Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Eduqas, Pearson Edexcel, AQA, OCR,

Difficulty level:   #### Worksheet Overview

What did one geometry book say to the other geometry book?

Don't look at me, I have my own set of problems! We don't have problems here only solutions.

The type of questions involving volume scale factor can appear problematic.

Honestly, they are not.  Smaller cubes length = 4 cm

Volume of the smaller cube = 64 cm³

Larger cubes length = 8 cm

What is the volume of the larger cube?

1.  Find the scale factor of the enlargement    8 ÷ 4  =  Scale factor 2

2.  THIS DOES NOT MEAN THAT THE VOLUME IS TWICE AS BIG.

3.  Take the scale factor and use it as if you were finding the volume i.e 2 x 2 x 2 = 8

4. The volume of the larger cube is 8 times as big

5. 64 x 8  = 512 cm³  Smaller rectangle length = 6  cm

Volume of the smaller rectangle = 60 cm³

Larger rectangle length = 18 cm

What is the volume of this cuboid rectangle?

1.  Find the scale factor of the enlargement    18 ÷ 6  =  Scale factor 3

2.  THIS DOES NOT MEAN THAT THE VOLUME IS THREE TIMES AS BIG.

3.  Take the scale factor and use it as if we were finding a volume. 3 x 3 x 3 = 27

4. The volume of the larger cuboid is 27 times as big

5. 27 x 60  = 1620 cm²

Let us put what we know already into a table

 Scale factor 2 Volume scale factor 2³ 4 times as big Scale factor 3 Volume Scale factor 3³ 27 times as big Scale factor 4 Scale factor 5

Can you spot the pattern and complete the rest of the table?

 Scale factor 2 Volume scale factor 2³ 8 times as big Scale factor 3 Volume scale factor 3³ 27 times as big Scale factor 4 Volume scale factor 4³ 64 times as big Scale factor 5 Volume scale factor 5³ 125 times as big

The volume of our skillset is increasing all the time.

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