You are constructing a closed rectangular box with a square base and a volume of 200 cubic inches. If the material for the base and lid costs 10 cents per square inch and the material for the sides costs 7 cents per square inch, express the cost of material for the box as a function of s, the length of the side of the base[/i]
story problem, please help
- Thread starter smsuski
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What have you tried?smsuski said:
Personally, I like simply to start writing things down, withotu a care int he world if it helps lead me to a solution. Whatever formula or definition comes to mind that might remotely be related to the problem.
s = length of side of square base.
h = height of box
s*s*h = box volume = 200 in<sup>3</sup> = s<sup>2</sup>*h
Top & Bottom Cost = $0.10*2*s<sup>2</sup>
Side Cost = $0.07*4*s*h
OK, now whwt?
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width: w
length: w (because the base is square)
height: h
volume: 200 = w<sup>2</sup>h
Solve the volume for "h=".
Write expressions for the surface areas of the various sides, in terms of "w" and "h". Multiply each expression by the appropriate "cost" factor. Use the "solving" part to substitute for "h".
(To be acceptable to your instructor, you might want to use a variable for the length instead of for the width, but since they're the same, it shouldn't matter.)
Eliz.
length: w (because the base is square)
height: h
volume: 200 = w<sup>2</sup>h
Solve the volume for "h=".
Write expressions for the surface areas of the various sides, in terms of "w" and "h". Multiply each expression by the appropriate "cost" factor. Use the "solving" part to substitute for "h".
(To be acceptable to your instructor, you might want to use a variable for the length instead of for the width, but since they're the same, it shouldn't matter.)
Eliz.