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Volume Scale Factor - Simple Problems

In this worksheet students will be able to find volume of similar shapes

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.

 

   cube         

 

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

 

 

          cuboid             

 

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

 

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