Question

The scale factor of a model of a swimming pool to the actual swimming pool is 1 to 20. The

Answer 1

Answer:

$0.05\ m^3$

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

$z^3=\frac{x}{y}$

we have

$z=\frac{1}{20}$

$y=400/ m^3$

substitute

$(\frac{1}{20})^3=\frac{x}{400}$

solve for x

$\frac{1}{8,000}=\frac{x}{400}$

$x=\frac{400}{8,000}$

$x=0.05\ m^3$