SOLUTION: An open-top box is to be constructed from a 4 foot by 6 foot rectangular cardboard by cutting out equal squares at each corner and folding up the flaps. Let x denote the length of

Algebra.Com
Question 77542: An open-top box is to be constructed from a 4 foot by 6 foot rectangular cardboard by cutting out equal squares at each corner and 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 and show the graph over the valid range of the variable x..

c) Using the graph, what is the value of x that will produce the maximum volume?


Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
An open-top box is to be constructed from a 4 foot by 6 foot rectangular cardboard by cutting out equal squares at each corner and folding up the flaps. Let x denote the length of each side of the square to be cut out.
:
The dimensions of the box will be (4-2x) by (6-2x) by x
:
a) Find the function V that represents the volume of the box in terms of x.
V = (4-2x)*(6-2x)*x
V = 4x^3 - 20x^2 + 24x
:
b) Graph this function and show the graph over the valid range of the variable x..

:
c) Using the graph, what is the value of x that will produce the maximum volume?
It is about .8 ft or about 9.6 inches.
Max vol would be 2.4 * 4.4 * .8 = 8.45 cu ft

RELATED QUESTIONS

1) An open-top box is to be constructed from a 4 foot by 6 foot rectangular cardboard by (answered by checkley71)
An open-top box is to be constructed from a 4 by 6 foot rectangular cardboard by cutting... (answered by Earlsdon)
An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting... (answered by ankor@dixie-net.com)
An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting... (answered by venugopalramana)
An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting... (answered by mukhopadhyay)
An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting... (answered by Earlsdon)
An open-top box is to be constructed from a 4 ft by 6 ft rectangular cardboard by cutting (answered by Earlsdon)
Please Help!!! I cant figure this out. 1) An open-top box is to be constructed from a (answered by ankor@dixie-net.com)
An open-top box is to be constructed from a 4 foot by 6 foot rectangular cardboard by... (answered by Nate,ankor@dixie-net.com)