IXL - Surface area and volume of prisms and cylinders: changes in scale (Geometry practice)

Look at this cube:

8 ft

If the side lengths are quadrupled, then how will the new volume compare to the old volume?

Write your answer as the ratio of two whole numbers separated by a colon; for example, "2:3".

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

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Learn with an example

question

Look at this cube:

1 in

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 4 times as long. Since the original side lengths were s, the new side lengths will be 4s. Calculate the volume:

V	=	(4s)³

	=	64s³

Divide the new volume by the original volume and simplify.

new volume

original volume

64s³

s³

Write the result as a ratio.

64 → 64:1

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

64:1

Looking for more? Try these:

Lesson: Surface area formulas

Lesson: Volume formulas

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Teacher tools

Work it out

Not feeling ready yet? These can help:

U.7Volume of prisms and cylinders

U.4Surface area of prisms and cylinders

L.1Understanding ratios

Lesson: Surface area formulas

Lesson: Volume formulas

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