Final answer:
To find the scale factor for a box with a volume of 10 cubic feet, you need the volume of an existing model as a reference. With that, the cube root of the volume ratio gives the scale factor, but the question lacks sufficient detail to calculate it directly.
Step-by-step explanation:
To determine the scale factor needed for a box with a volume of 10 cubic feet, we need to relate this desired volume to the volume of an existing model or to have a desired set of dimensions for the new box. Unfortunately, the question doesn't provide information about the original dimensions or model size to use as a reference. Without that baseline information, we cannot accurately compute a scale factor.
If, for instance, you have a smaller model of the box and you know its volume, you can use the cube root of the ratio of the desired volume to the model's volume to get the scale factor:
- Calculate the ratio of the desired volume to the model's volume (10 cubic feet / model's volume).
- Find the cube root of that ratio to get the scale factor.
This scale factor, when applied to each dimension of your model box, will give you a scaled-up or scaled-down box with the desired volume.