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The pair of figures are similar. Use the information given to find the scale factor of the figure on the left to the figure on the right.V = 576 mi³V = 9000 mi³SF =

The Pair Of Figures Are Similar Use The Information Given To Find The Scale Factor Of The Figure On The Left To The Figure On The RightV 576 MiV 9000 MiSF class=

Sagot :

When two figures are similar, the scale factor is given by the ratio between the measure of two corresponding lengths of the two figures.

[tex]r\propto R\implies R=kr[/tex]

Where k represents the scale factor.

Since the volume is a three dimensional measure(it is the product of three length units), the ratio between the volumes is the scale factor to the third power

[tex]R=kr\implies R^3=(kr)^3=k^3r^3\implies\frac{R^3}{r^3}=k^3[/tex]

Then, in our problem, the ratio between the volumes is:

[tex]\frac{576}{9000}=0.064[/tex]

Then, the scale factor is the cubic root of this ratio:

[tex]\sqrt[3]{0.064}=0.4[/tex]

The scale factor is 0.4.

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