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

Look at this sphere:

2 yd

If the radius is halved, then how will the new surface area compare to the old surface area?

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

The ratio of the new surface area to the old surface area will be .

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Learn with an example

question

Look at this sphere:

1 in

If the radius is tripled, 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 .

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

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.6Surface area of spheres

U.9Volume of spheres

L.1Understanding ratios

Lesson: Surface area formulas

Lesson: Volume formulas

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