SOLUTION: Suppose you have a rectangular sheet with width of 5in and length of 10in. You want to make an open-top box from this sheet by cutting out squares from each corner and folding up t

Algebra ->  Equations -> SOLUTION: Suppose you have a rectangular sheet with width of 5in and length of 10in. You want to make an open-top box from this sheet by cutting out squares from each corner and folding up t      Log On


   

Question 810933: Suppose you have a rectangular sheet with width of 5in and length of 10in. You want to make an open-top box from this sheet by cutting out squares from each corner and folding up the sides. Let the side of each square have length x in.
Find an expression in terms of x (in simplified form) of the volume of the open-top box. Let the volume be denoted by V(x).
Choose One:
a. V(x) = 50x - 15x^2 + x^3
b. V(x) = 50x - 30x^2 + 4x^3
c. V(x) = 50 - 15x + x^2
d. V(x) = 50 - 30x + 4x^2
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The sides of the base of that box will be 2x inches shorter than the original rectangular sheet,so the measurements of the box are
base length = 10-2x inches
base width = 5-2x inches
The height of the box will be x inches, so the volume in cubic inches is
V%28x%29=%2810-2x%29%285-2x%29x
V%28x%29=%2850-20x-10x%2B4x%5E2%29x
V%28x%29=%284x%5E2-30x%2B50%29x
highlight%28V%28x%29=4x%5E3-30x%5E2%2B50x%29 with the polynomial in standard form.
OR
V%28x%29=%2850-20x-10x%2B4x%5E2%29x
V%28x%29=%2850-30x%2B4x%5E2%29x
highlight%28V%28x%29=50x-30x%5E2%2B4x%5E3%29 (answer b) for those who do not care about standards.