calculus
posted by DJ .
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.

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,, :)
Respond to this Question
Similar Questions

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 … 
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 … 
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? 
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. 
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 … 
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 … 
Advance Algebra
An open box is to be made from a rectangular piece of tin 12 inches long and 10 inches wide by cutting pieces of xinch square from each corner and bending up the sides. a. Find a formula that expresses the volume V of the box as a … 
Math
A square sheet of cardboard 100 cm by 100 cm is to have corners of side length x cut out. These cutouts will create flaps that can be folded up to form a box with no lid. The length and width of the base of the box are given by the … 
Calculus PLEASE HELP
A rectangular piece of tin has an area of 1334 square inches. A square tab of 3 inches is cut from each corner, and the ends and sides are turned up to make an open box. If the volume of the box is 2760 cubic inches, what were the … 
Math
A machine produces open boxes using rectangular sheets of metal (12in by 20in). The machine cuts equalsized squares from each corner, and then shapes the metal into an open box by turning up the sides. Express the volume of the box …