elementary algebra

[Rani]

A cubic storage box is made with 96 square feet of wood. What is the length of each edge?

 

[tkhunny]

s = length of one edge.

\(\displaystyle s^{2} \)is the area of one side

There are six sides.

Now what?

 

[Someone2841]

A cubic storage box is made with 96 square feet of wood. What is the length of each edge?

This knowledge is essential to solving this problem:

\(\displaystyle A(s) = 6s^{2}\)

That is, the surface area \(\displaystyle A\) of a cube is equal to 6 times the square of one edge length \(\displaystyle s\). This is logical because a cube has equal edges (again, with length \(\displaystyle s\)) and six faces. Therefore, each face has area \(\displaystyle s^{2}\), and since there are six of them, six times one face's surface area will get you the total surface area.


Now, this is only the starting formula. What we need is to define \(\displaystyle s\) in terms of \(\displaystyle A\). Start by dividing by six to get \(\displaystyle \frac{1}{6}A(s) = s^{2}\), then take the square root: \(\displaystyle \sqrt{\frac{1}{6}A(s)} = s\). Finally, define s as a function of A:

\(\displaystyle s(A) = \sqrt{\frac{1}{6}A}\)

That is, and the edge length \(\displaystyle s\) of a cube with surface area \(\displaystyle A\) is equal to the square root of one sixth \(\displaystyle A\).

Therefore, \(\displaystyle s(96) = \sqrt{\frac{1}{6}96} = 4\).
[Note, another valid mathematical solution could have been -4; however, since we are dealing with a physical scaler quantity (i.e., direction is not taken into account, only the magnitude), negative numbers don't really "exist". We therefore consider -4 to be an extraneous solution to the problem.]

 

[tkhunny]

This knowledge is essential to solving this problem:

\(\displaystyle A(s) = 6s^{2}\)

Yes, and one can either use ones brain and figure it out or such information can just drop out of the sky. {shakes head}

 

[mmm4444bot]

Hi Rani:

If you do not understand the notation \(\displaystyle A(s)\), do not be concerned.

It is called "function notation", and you will learn about it in a future math course.

For now, you may simply interpret A(s) in the post above as a special way of writing the variable "Area".

Cheers ~ Mark :cool: