The radius of the large sphere is 3 times longer than the radius of the small sphere. How many times smaller than the volume of the large sphere is the volume of the small sphere?

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irspow irspow · Answer 1 · 2017-03-21T15:04:42+01:00

V=(4p(3r)^3)/3 and v=(4pr^3)/3

V/v=(3r)^3/(r^3)

V/v=9r^3/r^3

V/v=9

So the smaller sphere has a volume that is nine times smaller than the larger.

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calculista calculista · Answer 2 · 2019-02-09T23:18:48+01:00

Answer:

The volume of the smaller sphere is [tex]27[/tex] times smaller than the volume of the larger sphere

Step-by-step explanation:

we know that

If two figures are similar then, the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-------> the scale factor

x-------> the volume of the larger sphere

y-------> the volume of the smaller sphere

so

[tex]z^{3}=\frac{x}{y}[/tex]

In this problem we have

[tex]z=3[/tex]

substitute

[tex]3^{3}=\frac{x}{y}[/tex]

[tex]27=\frac{x}{y}[/tex]

[tex]y=x/27[/tex] -----> The volume of the smaller sphere is [tex]27[/tex] times smaller than the volume of the larger sphere

or

[tex]x=27y[/tex] -----> The volume of the larger sphere is [tex]27[/tex] times greater than the volume of the smaller sphere