IXL | Volume: changes in scale II

Look at this sphere:

5 yd

If the radius 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

4:1

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

8:1

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Learn with an example

question

Look at this sphere:

5 yd

If the radius is doubled, 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

times the old volume.

The new volume will be

times the old volume.

The new volume will be

times the old volume.

solution

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

The original sphere had this volume:

𝜋

The new sphere will have 2 times the radius. Since the original radius was r, the new radius will be 2r. Calculate the volume:

𝜋

(

)

𝜋

Divide the new volume by the original volume and simplify.

new volume

original volume

𝜋

The new volume will be

times the old volume.

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Volume: changes in scale I

W.7Volume of spheres

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