HELP ME PLEASE.
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

HELP ME PLEASE. 
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.

anonymous · Answer

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anonymous · Answer

PLEASE HELP ME !?

anonymous · Answer

Well, for it to be similar I would say to just apply the change to one side of the box to all sides of the box. i.e. 2ft went to 6ft (which is multiplying it by 3). I would just multiply the other 2 sides by 3 to get the length of the other 2 sides.

anonymous · Answer

That's kind of confusing.

anonymous · Answer

$$2\times3=6$$$$0.5\times3=?$$$$1\times3=?$$Just scaling all sides by 3. As they have done with the one given side. This will give the box a similar shape but it will be larger in all dimensions.

anonymous · Answer

2 x 3 = 6
0.5 x 3 = 1.5
1 x 3 = 3 
so do i add all those up together to get the awnser ?

anonymous · Answer

That will give you the dimensions of the larger box. Do you know the formula for the volume of that shape?

anonymous · Answer

2 * ( length + width ) ?

anonymous · Answer

$$Volume=length \times width \times height$$

anonymous · Answer

Oh alright

anonymous · Answer

So what's the volume of the small box and what's the volume of the big box?

anonymous · Answer

The volume of the small box is 1 ?

anonymous · Answer

Correct, and what is the volume of the large one?

anonymous · Answer

9.18 ?

anonymous · Answer

not quite, what did you multiply to get that?

anonymous · Answer

2 x 3 = 6
0.5 x 3 = 1.5
1 x 3 = 3 
so i multiplied 6 x 1.5 x 3

anonymous · Answer

You have the right method but:$$6\times1.5\times3\neq9.18$$You should get:$$6\times1.5\times3=27$$

anonymous · Answer

oh okay so what would be the next step?

anonymous · Answer

27 is the volume of the larger box (which is your answer). So you can take all the working here and write it up real nice. As for the scale factor rule of volume try to follow this. If you scale a box by a scale 'b' then the volume will scale at:$$V=V _{0} \times b^3$$Where V0 is the volume of the original box and V is the volume of the new box.
For example, the box we had, had initial volume 1, so V0=1. The length went from 2 to 6 so it was scaled by a factor of 3, so b=3.
Therefore:$$V=1 \times 3^3$$$$V=1 \times 27$$$$V=27$$Like we calculated, cool huh? :)

anonymous · Answer

thank you so much (: