IXL | Volume: changes in scale

Look at this rectangular prism:

9 cm

4 cm

3 cm

If the height is doubled, then which of the following statements about its volume will be true?

The ratio of the new volume to the old volume will be

3:1

The ratio of the new volume to the old volume will be

1:2

The ratio of the new volume to the old volume will be

4:1

The ratio of the new volume to the old volume will be

2:1

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Learn with an example

question

Look at this cube:

2 cm

If the side lengths are doubled, then which of the following statements about its volume will be true?

The ratio of the new volume to the old volume will be

2:1

The ratio of the new volume to the old volume will be

16:1

The ratio of the new volume to the old volume will be

64:1

The ratio of the new volume to the old volume will be

8:1

solution

You can solve this problem without using the measurements given in the diagram.

The original cube had this volume:

V = s³

The new cube will have sides that are 2 times as long. Since the original side lengths were s, the new side lengths will be 2s. Calculate the volume:

V	=	(2s)³

	=	8s³

Divide the new volume by the original volume and simplify.

new volume

original volume

8s³

s³

Write the result as a ratio.

8 → 8:1

The ratio of the new volume to the old volume will be

8:1

$Confetti$

Excellent!

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Work it out

Not feeling ready yet? This can help:

HH.1Volume of cubes and rectangular prisms

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