High School

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------------------------------------------------ A prism with a volume of 3125 ft³ is scaled down to a volume of 200 ft³.

What is the scale factor?

Enter your answer as a decimal or a fraction in simplest form in the box.

Answer :

Answer:

The scale factor is equal to [tex]0.4[/tex] or [tex]\frac{2}{5}[/tex]

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 dilated prism

y------> the volume of the original prism

so

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

we have

[tex]x=200\ ft^{3}[/tex]

[tex]y=3,125\ ft^{3}[/tex]

substitute

[tex]z^{3}=\frac{200}{3,125}[/tex]

[tex]z=\sqrt[3]{\frac{200}{3,125}}[/tex]

[tex]z=0.4[/tex] or [tex]z=\frac{2}{5}[/tex]
the right answer is 2/5

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