math question? dealing with surface area to volume?

Question

okay the question is

find the surface area to volume ratio for each of the following:


a rectangular prism with the dimensions of n*n*1
(*=multiplied by)
i have the answer but i cant get how it looks worked out, the answer is 2+ 4/n (read as two plus 4 over n)

um also could someone use the surface area formula plz:)

Answer 1

The V is n x n x 1 or nn (would be easier to write if we had access to the square superscript)

The six surfaces make up total area, A.
Two faces are n x n each, the other four are n x 1 each.
Total A is 2( n x n) + 4 (n x 1) = 2nn + 4n = n(2n + 4)

Ratio A/V is n(2n +4) / nn = (2n + 4)/n

Answer 2

The volume is:

V = length x width x height

V = n x n x 1 = n²

The surface area is:

SA = 2 x area of bottom/top + 2 x area of left/right sides + 2 x area of front/back sides

The area of the top and bottom is nxn = n², and the area of each of the 4 sides is 1xn = n.

So the surface area is: 2n² + 4n

The ratio then is:

(2n² + 4n)/n² = 2n²/n² + 4n/n² = 2 + 4/n

Answer 3

the derivative of volume is the surface area
your volume is n^2 (n squared)
so your surface area is 2n (two times n).