Question

A box with a square base and open top must have a volume of 48668 cm3 . We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x , the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x .] Simplify your formula as much as possible.

Answer 1

Answer:

Step-by-step explanation:

Given that a box with a square base and  open top has volume = 48668 cm^3

i.e. if x is the side of square and h the height then

$x^2h = 43668\\h=\frac{43668}{x^2}$

Surface area of open box = area of base + area of 4 sides

=$x^2 +4xh =x^2+4x(\frac{43668}{x^2})\\=x^2+\frac{43668*4}{x}$

Thus we get

Surface area in terms of x as

$x^2+\frac{43668*4}{x}$