Thread: 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?

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 " "

Now look at a side of the die, it is a square with edges of 1 ft. The area of the side is , or 1 square foot.

Now look at the entire die. It is a cube with edges of 1ft. The volume of that cube is or "one cubic foot"

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

Hey, good answer.

What comes after 3-dimensions?

Originally Posted by symmetry

Hey, good answer.

What comes after 3-dimensions?

Think of invisible dice... and we'll just say that's a hypercube

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

Your thoughts?

Originally Posted by symmetry

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

Your thoughts?

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)

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!

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.

I will surely never take such courses.

Thanks!