Answer:
[tex]0.05\ m^3[/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 model of a swimming pool
y ---> the volume of the actual swimming pool
so
[tex]z^3=\frac{x}{y}[/tex]
we have
[tex]z=\frac{1}{20}[/tex]
[tex]y=400/ m^3[/tex]
substitute
[tex](\frac{1}{20})^3=\frac{x}{400}[/tex]
solve for x
[tex]\frac{1}{8,000}=\frac{x}{400}[/tex]
[tex]x=\frac{400}{8,000}[/tex]
[tex]x=0.05\ m^3[/tex]
