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
Algebra ->
Formulas
-> 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
Log On
Question 26229: 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.
b) Graph this function.
c) Using the graph, what is the value of x that will produce the maximum volume?
You can put this solution on YOUR website! An open-top box is to be connected from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and then folding up the flaps. Let x denote the length of each side of the square to be cut out. Find the function V that represents the volume of the box in terms of x.
This is what I got:
6x+8x+x=14x²
x=14
LENGTH OF BOARD=6 FT....WIDTH OF BOARD =8 FT.
IF X LONG SQUARE PIECES ARE CUT AT 4 CORNERS WE SHALL HAVE THE BOX DIMENSIONS AS
HEIGHT =X.....LENGTH = 6-2X.....WIDTH =8-2X
VOLUME = V = L*W*H =X(6-2X)(8-2X)=X(48-28X+4X^2)=48X-28X^2+4X^3
THE GRAPH WILL LOOK LIKE THIS
FROM THE GRAPH YOU CAN SEE V HAS A PEAK AT X=ABOUT 3.5 FEET
