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The scale factor of a model of a warehouse to the actual warehouse is 1 to 2. The volume of theactual warehouse is 8,455 ft^3. Find the volume of the model. Round to a whole number.

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Question

The scale factor of a model of a warehouse to the actual warehouse is 1 to 2. The volume of the actual warehouse is 8,455 ft^3. Find the volume of the model. Round to a whole number.​

Solution

The scale factor (or ratio) of the model to the actual is

[tex]1\colon2[/tex]

The scalar factor (or ratio) for the volume will be

[tex]\begin{gathered} 1^3\colon2^3 \\ 1\colon8 \end{gathered}[/tex]

To find the volume of the model

Let the volume of the model by denoted with x

We use the ratio

[tex]\begin{gathered} \frac{1}{8}=\frac{x}{8455} \\ \text{cross multiply} \\ 8\times x=1\times8455 \\ 8x=8455 \\ x=\frac{8455}{8} \\ x=1056.875 \\ x=1057ft^3\text{ (to the nearest whole number)} \end{gathered}[/tex]

Thus, the volume of the model is 1057ft^3

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