SOLUTION: An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of e
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Question 52767: An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out.
a) Find the function V that represents the volume of the box in terms of x.
You can put this solution on YOUR website! An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out.
:
a) Find the function V that represents the volume of the box in terms of x.
:
The bottom dimensions: [8-2x] by [6-2x]; the height would be just 'x'
:
Vol = Length * Width * Height
Vol = [8-2x] * [6-2x] * x
:
FOIL Length * Width
Vol = [48 - 28x + 4x^2] * x
:
Mult that by x (height) and you have
Vol = 48x - 28x^2 + 4x^3
:
V(x) = 4x^3 - 28x^2 + 48x
An example: a box 1 ft high: [8-2] * [6-2] * 1 = 24 cu ft.
:
Check our equation for x=1: substitute 1 for x in the equation and you have: 4 - 28 + 48 = +24.
Make sense to you?
