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.

Question

anonymous · Answer

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anonymous · Answer

The two ‘this side up’ sides correspond, so you can work out the scale from these two figures. If you divide 6ft by 2ft you get 3, so you know that to get the measurements of the other two sides of the larger box, you have to multiply the corresponding sides on the smaller box by 3. Use this to work out the length, width and breadth of the larger box, and then multiply them all togeth to get the volume ☺

anonymous · Answer

But that method doesn't use the scale factor rule of volume :/

anonymous · Answer

If you need to use the scale factor rule of volume:
The volume of the smaller box is 2*0.5*1=1
To get the volume of the larger box, you have to multiply the smaller box’s volume by the scale factor (3) cubed.
3 cubed is 27, so you multiply the smaller box's volume by 27:
1*27=27.

I’m not really sure how to fully explain why you have to multiply by the scale factor cubed, sorry!