IXL | Volume: changes in scale I

Look at this rectangular prism:

3 ft

8 ft

1 ft

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

The new volume will be

times the old volume.

The new volume will be

of the old volume.

The new volume will be

times the old volume.

The new volume will be

times the old volume.

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Learn with an example

question

Look at this rectangular prism:

5 mm

9 mm

6 mm

If the height is tripled, 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

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

solution

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

The original rectangular prism had this volume:

V = lwh

The new rectangular prism will have 3 times the height. Since the original height was h, the new height will be 3h. Calculate the volume:

V	=	lw(3h)

	=	3lwh

Divide the new volume by the original volume and simplify.

new volume

original volume

3lwh

lwh

Write the result as a ratio.

3 → 3:1

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

3:1

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Work it out

Not feeling ready yet? These can help:

CC.5Volume of cubes and prisms

L.1Understanding ratios

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