Volume Scale Factor - Simple Problems Worksheet

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

The volume of our skillset is increasing all the time.

These two prisms are similar

Smaller Prism - Base 3 cm

Volume of the Smaller Prism = 45 cm²

Larger Prism - Base 9 cm

What is the volume of the larger prism?

405 cm²

135 cm³

1215 cm³

1456 cm³

These cuboids are similar. What is the volume of the larger cuboid?

cuboid

Small cuboid side length 6 cm

Volume = 96 cm³

cuboid

Larger cuboid side length 24 cm

405 cm²

135 cm³

1215 cm³

1456 cm³

cuboid

Small cube has sides of 2 cm, the larger cube has side 5 times bigger.

The volume of the smaller cube is 8 cm³

What is the volume of the larger cube?

405 cm²

135 cm³

1215 cm³

1456 cm³

swimming pool

The volume of water in this swimming pool is 1000 m³

The length of its side is 20 m.

Another swimming pool has a length of side 30 m.

What is the volume of water in the other swimming pool?

1500 m³

1750 m³

2750 m³

3375 m²

brick brick

These two bricks are mathematically similar.

The larger brick has a side length of 12 cm. The smaller brick has a side length of 4 cm.

The volume of the larger brick is 144 cm³

Calculate the volume of the smaller brick.

	50.3 cm³	55.3 cm³	5.33 cm³	3.53³
Volume of the smaller brick

The volume of this can is 330 ml.

The can is 6 cm high.

In a promotion, another can that is 1.5 times bigger is put on sale.

What is the volume of the cola in the larger can?

1115 cm³

1005 cm³

1255.75 cm³

1113.75 cm³

cube

These two cubes are mathematically similar.

The side of the smaller cube is 4 cm and the side of the larger cube is 12 cm.

The volume of the larger cube is 864 cm³

What is the volume of the smaller cube?

1115 cm³

1005 cm³

1255.75 cm³

1113.75 cm³

rugby ball

This rugby ball has a length of 8 cm and a total volume of 90 cm²

A similar rugby ball has a length of 16 cm.

What is its volume?

1115 cm³

1005 cm³

1255.75 cm³

1113.75 cm³

cylinder

These two cylinders are mathematically similar.

The radius of the larger cylinder is 15 cm and the radius of the smaller cylinder is 5 cm.

The total volume of the smaller cylinder is 200 cm³

Calculate the volume of the larger cylinder.

1115 cm³

1005 cm³

1255.75 cm³

1113.75 cm³

ANSWERS

Question 1

These two prisms are similar

Smaller Prism - Base 3 cm

Volume of the Smaller Prism = 45 cm²

Larger Prism - Base 9 cm

What is the volume of the larger prism?

CORRECT ANSWER

1215 cm³

EDDIE SAYS

First, find the scale factor 9 ÷3 = 3 Find volume scale factor 3 x 3 x 3 = 27 Remember it is not 3 times as big The volume of the larger prism is 27 times as big! 45 x 27 = 1215 cm³ That's a lot bigger, isn't it?

ANSWERS

Question 2

These cuboids are similar. What is the volume of the larger cuboid?

cuboid

Small cuboid side length 6 cm

Volume = 96 cm³

cuboid

Larger cuboid side length 24 cm

CORRECT ANSWER

EDDIE SAYS

Scale factor 24 ÷ 6 = 4 Scale factor 4x 4 x 4 = 64 The volume is 64 times larger 96 x 64 = 6144 cm³ Are you getting the hang of cubing the scale factor first?

ANSWERS

Question 3

cuboid

Small cube has sides of 2 cm, the larger cube has side 5 times bigger.

The volume of the smaller cube is 8 cm³

What is the volume of the larger cube?

CORRECT ANSWER

EDDIE SAYS

Practice is all it takes! The question tells us that the scale factor is 5, job done. Volume scale factor is 5 x 5 x 5 = 125 Volume is 125 times as big. 8 x 125 = 1000 cm³ Working with numbers is magic, don't you think?

ANSWERS

ANSWERS

Question 5

swimming pool

The volume of water in this swimming pool is 1000 m³

The length of its side is 20 m.

Another swimming pool has a length of side 30 m.

What is the volume of water in the other swimming pool?

CORRECT ANSWER

3375 m²

EDDIE SAYS

Let's dive into this one! Scale factor 30 ÷ 20 = 1.5 Volume Scale Factor =1.5³ = 3.375 1000 x 3.375 = 3375 m³ Don't let decimals put you off. We deal with them the same way. I am off to cool down now!

ANSWERS

Question 6

brick brick

These two bricks are mathematically similar.

The larger brick has a side length of 12 cm. The smaller brick has a side length of 4 cm.

The volume of the larger brick is 144 cm³

Calculate the volume of the smaller brick.

CORRECT ANSWER

	50.3 cm³	55.3 cm³	5.33 cm³	3.53³
Volume of the smaller brick

EDDIE SAYS

Are you building up your skillset now? What looks daunting as a question is not so bad once you can break it down. Scale factor 12 ÷ 4 = 3 Volume scale factor is 3³ = 27 The volume of the small brick is 27 times smaller 144 ÷ 27 = 5.33 cm³ I don't fancy dropping that brick on my foot do you?

ANSWERS

Question 7

The volume of this can is 330 ml.

The can is 6 cm high.

In a promotion, another can that is 1.5 times bigger is put on sale.

What is the volume of the cola in the larger can?

CORRECT ANSWER

1113.75 cm³

EDDIE SAYS

This is thirsty work isn't it? We are lucky here because the scale factor has already been given. Volume scale factor is 1.5³ = 3.375 330 x 3.375 = 1113.75 cm³ Cheers!