1. ## Open Box

An open box with a square base is required to have a volume of 10 cubic feet.

NOTE: What exactly is a cubic foot?

(a) Express the amount A of material used to make such a box as a function of the length x of a side of the square base.

(b) How much material is required for a base 1 foot by 1 foot?

NOTE: Is one foot by foot the same as 144 inches?

2. Originally Posted by symmetry
An open box with a square base is required to have a volume of 10 cubic feet.

NOTE: What exactly is a cubic foot?
Hmmm. Imagine you have a pair of foot-long die (or a pair of dice, it doesn't matter). The length of the edge of the die is 1 foot, you would write that as " $\text{length}=1\text{ft.}$"

Now look at a side of the die, it is a square with edges of 1 ft. The area of the side is $\text{Area}=1\text{ft.}^2$, or 1 square foot.

Now look at the entire die. It is a cube with edges of 1ft. The volume of that cube is $\text{Volume}=1\text{ft.}^3$ or "one cubic foot"

So foot is 1-dimensional
feet squared is 2-dimensional
and feet cubed is 3-dimensional

3. ## ok

What comes after 3-dimensions?

4. Originally Posted by symmetry

What comes after 3-dimensions?
Think of invisible dice... and we'll just say that's a hypercube

5. ## ok

Someone one said that anything beyond 3-dimensions is the spirit world.

6. Originally Posted by symmetry
Someone one said that anything beyond 3-dimensions is the spirit world.

They have not met a topologist.

Since we are 3-dimensional, we can't see a 4-dimensional object, however scientist think that the universe is a 4-dimensional object (so we might be in the middle of a 4-dimensional sphere)

7. ## ok

I've heard of topology.

I often hear nightmare stories about topology courses.

I will try to stay away from such concepts.

I have enough trouble understanding basic math much less topology.

Thanks!

8. Originally Posted by symmetry
I've heard of topology.

I often hear nightmare stories about topology courses.

I will try to stay away from such concepts.

I have enough trouble understanding basic math much less topology.

Thanks!
Well topologists even confuse themselves, they can't even tell the difference between their coffee mug and their donut in the morning...

B.T.W. that was a topologist joke, since a donut (torus?) and a mug are technically the same shape in topology.

9. ## ok

I will surely never take such courses.

Thanks!