The relationship between the side length of a be and the volume of the cube is shown in the table. Determine if the relationship is proportional using two different methods. Explain your reasoning. (Draw a graph, let y-axis be the volume of the cube and let the x-axis be the side length)

Question

calculusxy · Answer

attachment

calculusxy · Answer

@satellite73

anonymous · Answer

evidently the volume of a cube is the ... cube!
hence the name, i.e. that is why $x^3$ is called "x cubed" rather than "x to the third power"

calculusxy · Answer

I used both a table and a graph to show the two methods. Will this be fine?

calculusxy · Answer

I saw that this was clearly not proportional because
1) even if the line started from the origin, 
2) it was not straight

anonymous · Answer

it is not proportional for sure $$A=x^3$$ is not a line

calculusxy · Answer

However, I made this table where if x= 2 (length) then the volume (ft^3) is 6.

calculusxy · Answer

I am not sure if that will be valid.

anonymous · Answer

One way is to graph it and show that it is not a line

anonymous · Answer

you lost me 
$$2^3=8$$ not $6$

calculusxy · Answer

Oh yes correct @satellite73

calculusxy · Answer

Yes I did that @wio

anonymous · Answer

Another way is to graph V/l and then show that that is not constant.

calculusxy · Answer

But will it be okay that I used a table for the second method because tables are used to guide someone in plotting the coordinates.

anonymous · Answer

I.E. not horizonatal

anonymous · Answer

You can use a table

anonymous · Answer

But if you're going to say "it's not a line" with the table, you're using the same reasoning

calculusxy · Answer

Okay thanks for that help. Can you help me with some other questions? I have a quiz tmrw and I need some guideline.

calculusxy · Answer

I will give a new post.

anonymous · Answer

I think your table should include V/l or something.

calculusxy · Answer

Wait.. I am going to show you my table..

anonymous · Answer

ok

calculusxy · Answer

attachment

calculusxy · Answer

So that was my table.

anonymous · Answer

Okay?

calculusxy · Answer

Yet this table is not continuous. I have represented this table in a graph and have shown that this is not proportional.

anonymous · Answer

It doesn't need to be continuous

anonymous · Answer

But the table isn't really showing anything

anonymous · Answer

I think you should include another row,  (Volume/Length)

anonymous · Answer

Can you do that?

anonymous · Answer

Then you will get  1, 4, 9

anonymous · Answer

Which shows that proportion is not constant

calculusxy · Answer

Oh okay.

calculusxy · Answer

Thanks for that suggestion :)