IXL | Volume: changes in scale II

Look at this sphere:

2 cm

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

27:1

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

1:8

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:

10 cm

If the radius 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

9:1

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

81:1

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

27:1

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

3:1

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 3 times the radius. Since the original radius was r, the new radius will be 3r. Calculate the volume:

𝜋

(

)

𝜋

36𝜋r³

Divide the new volume by the original volume and simplify.

new volume

original volume

36𝜋r³

𝜋

Write the result as a ratio.

27 → 27:1

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

27:1

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Volume: changes in scale I

W.7Volume of spheres

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