# calculus

posted by .

Find the formula for the described function and state its domain. An open rectangular box with a volume of 8 cubic meters has a square base. Express the surface area of the box as a function of S(x) of the length x of a side of the base.

• calculus -

from the volume,
8 = x * x * h
h = 8/(x^2)
therefore,
surface area = 2lw + 2lh + 2wh
where l=length, w=width, h=height
since it's an open box:
S(x) = x^2 + 2[8/(x^2)](x) + 2[8/(x^2)](x)
S(x) = x^2 + 32/x

so there,, :)

## Similar Questions

1. ### math

A box with a rectangular base and rectangular sides is to be open at the top. It is to be constructed so that its width is 8 meters and its volume is 72 cubic meters. If building this box costs \$20 per square meter for the base and …
2. ### Calculus

I actually have two questions: 4. An open box is to be made from a rectangular piece of material 3m by 2m by cutting a congruent square from each corner and folding up the sides. What are the dimensions of the box of the largest volume …
3. ### Calc

A rectangular box, with a square base and open at the top is to be constructed. If the volume of the box needs to be 108 cubic feet, what is the minimum surface area?
4. ### algebra

have 50 sq ft of material to make an open top box with a square base. a) use formula for surface area to express the height h of the box in terms of x. b) find the dimensions of the box that will produce the maximum volume.
5. ### Pre Calculus

1. A rectangular box has a square base, four sides, but no top. It has a volume of 20 cubic feet. Let A be the surface area of the box, and L the length of one side of the base. (a) The volume is measured in cubic feet. What units …
6. ### Calculus

An OPEN box has a square base and a volume of 108 cubic inches and is constructed from a tin sheet. Find the dimensions of the box, assuming a minimum amount of material is used in it's construction. HINT: the goal is to minimize the …