Question

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

volume of the actual pool is 400 m^3 .
What is the volume of the model?

20m^3
0.05m^3
1m^3
0.15m^3​

Answer 1

0.05m^3

Explanation:

Got it right on the test.

Answer 2

`0.05\ m^3`

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=(x)/(y)`

we have

`z=(1)/(20)`

`y=400/ m^3`

substitute

`((1)/(20))^3=(x)/(400)`

solve for x

`(1)/(8,000)=(x)/(400)`

`x=(400)/(8,000)`

`x=0.05\ m^3`