The Right Move home-moving company has a variety of cardboard packing boxes available for use. The packing boxes shown here are similar figures. What is the volume of the larger box? Show your work and explain how you arrived at your answer by applying the scale factor rule of volume.
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Well, by what you said we know they are similar, right? If they are similar then the ratio of one side of one box to the corresponding side of the other box is the same for all sides of the box. We know one side of the bigger box is 6, and the corresponding (the side that is the same side on the smaller box) is 2. So to get from the side of the smaller box (2) to the side of the bigger box (6) you multiply by 3. So, since this 3 is the scale factor. Since it is always the same do that same thing for all sides of small box to find the other sides of the bigger box. So the three sides of the bigger box will be:
The volume of the small box is length*width*height, so that is 2*.5*3=3
The volume of the bigger box is length*width*height, so that is 6*1.5*3=27.