Question

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.

Answer 1

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

`1\colon2`

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

`\begin{gathered} 1^3\colon2^3 \\ 1\colon8 \end{gathered}`

To find the volume of the model

Let the volume of the model by denoted with x

We use the ratio

`\begin{gathered} (1)/(8)=(x)/(8455) \\ \text{cross multiply} \\ 8* x=1*8455 \\ 8x=8455 \\ x=(8455)/(8) \\ x=1056.875 \\ x=1057ft^3\text{ (to the nearest whole number)} \end{gathered}`

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