Help Me Comprehend This.... (change of units)

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The discussion centers around converting cubic feet to cubic inches, specifically questioning the conversion of 3 cubic feet of stuffing. The correct calculation reveals that 3 cubic feet equals 5,184 cubic inches, derived from multiplying 3 by 12 cubed (3 x 12 x 12 x 12). The confusion arises from misunderstanding dimensional changes, as the quantity in cubic inches is significantly larger than in cubic feet due to the three-dimensional nature of the measurement. Visualizing the conversion with physical cubes helps clarify the relationship between the units. Ultimately, the explanation provided resolves the initial misunderstanding about the conversion process.
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Hello,

First off, I apologize if this is in the wrong section. I didn't think this would constitute as a homework problem,as I'm not really asking to solve a problem,but more, I'm asking you all to help me comprehend and mentally vizualize this.

So I had a story problem that went along the lines of this:

"I Have 3ft^3 of stuffing for a project,but the project requires that the quantity be in cubic inches. How many In^3 do i have?"

Now,ultimately, the answer was 5,184"

Using the formula-3×12×12×12

Is it just me,or does this seem wrong?

I feel that the answer would be 36 cu.in. in the sense that the quantity is the same,only stated in inches rather than feet.

Can anyone help me comprehend this somehow? Am I just not thinking 3 dimensionally? Or am I in the right here?

Appreciate it in advance.

-ProjectTruth
 
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If you have 1 cubic feet, how many cubic inches do you have?
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If you have 3 cubic feet, how many cubic inches do you have?
If you have 4 cubic feet, how many cubic inches do you have?
 
ProjectTruth said:
Hello,

First off, I apologize if this is in the wrong section. I didn't think this would constitute as a homework problem,as I'm not really asking to solve a problem,but more, I'm asking you all to help me comprehend and mentally vizualize this.

So I had a story problem that went along the lines of this:

"I Have 3ft^3 of stuffing for a project,but the project requires that the absolute quantity be in cubic inches. How many In^3 do i have?"

Now,ultimately, the answer was 5,184"

Using the formula-3×12×12×12

Is it just me,or does this seem wrong?

I feel that the answer would be 36 cu.in. in the sense that the quantity is the same,only stated in inches rather than feet.

Can anyone help me comprehend this somehow? Am I just not thinking 3 dimensionally? Or am I in the right here?

Appreciate it in advance.

-ProjectTruth

The easiest way to do dimensional changes is by multiplying by "1", so that the quantity changes correctly along with the units.

1 foot = 12 inches, so do this:

3 ft^3 * (12in/ft)^3 = 3 * 1728 ft^2 in^3 / ft^3 = 5184 in^3
 
To help with visualisation:

Imagine a cubic inch as a physical cube with 1 inch sides.

You need 12 such cubes to make a line of 1 foot length and 1 inch both in height and width.
You need to stack 12 such lines one on top of another to get a wall of 1 foot length and height, but still one inch in width.
You need 12 such walls one next to another to make a cube 1 foot by 1 foot by 1 foot.
You need 3 such cubes to get 3 cubic feet.
 
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Bandersnatch said:
To help with visualisation:

Imagine a cubic inch as a physical cube with 1 inch sides.

You need 12 such cubes to make a line of 1 foot length and 1 inch both in height and width.
You need to stack 12 such lines one on top of another to get a wall of 1 foot length and height, but still one inch in width.
You need 12 such walls one next to another to make a cube 1 foot by 1 foot by 1 foot.
You need 3 such cubes to get 3 cubic feet.

This was very helpful actually,and was exactly what I was looking for.

Thanks to all other participants.

Cheers.
 
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