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

The answer is 0.05 m^3

Step-by-step explanation:

What is a scale factor? It is a ratio that is used to relate a model dimensions to the actual dimensions.

For the question above the scale factor is given as 1:20, which means that every 1m length on the model swimmimg pool translates to 20m length of the actual swimming pool.

Since  the given scale factor 1:20 only gives the dimension ratio for length and we are looking for the volume we have to derive out own volume scale ratio.

To derive our volume scale ratio we have to cube or raise the scale factor by exponent 3 => (1:20)^3

Volume Scale Factor = 1:8000, which means  1m^3 on the model swimming pool translates to 8000m^3 of the actual swimmimg pool.

So if given the actual swimming pool volume has 400m^3, our model swimming pool => 400/8000 = 0.05m^3.

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