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

[ProjectTruth]

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

 

[Vanadium 50]

If you have 1 cubic feet, how many cubic inches do you have?
If you have 2 cubic feet, how many cubic inches do you have?
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?

 

[berkeman]

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:

$$3 ft^3 * (12in/ft)^3 = 3 * 1728 ft^2 in^3 / ft^3 = 5184 in^3$$

 

[Bandersnatch]

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.

 

[ProjectTruth]

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.