SOLUTION: A box with an open top is constructed from a rectangular piece of cardboard which is initially 30 inches long and 23 inches wide. The box will be formed by removing squares of leng
Algebra.Com
Question 567351: A box with an open top is constructed from a rectangular piece of cardboard which is initially 30 inches long and 23 inches wide. The box will be formed by removing squares of length x inches from each corner and then folding up the sides (as shown below). Express the volume (V) of the box as a function of x.
I've been trying to figure out this problem for a while, any help is greatly appreciated!!! Thanks!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A box with an open top is constructed from a rectangular piece of cardboard which is initially 30 inches long and 23 inches wide.
The box will be formed by removing squares of length x inches from each corner and then folding up the sides (as shown below).
Express the volume (V) of the box as a function of x.
:
From the information, the box dimensions will be:
(30-2x) by (23-2x) by x (Height)
:
therefore the volume:
V(x) = x*(30-2x)*(23-2x)
FOIL
V(x) = x(690 - 60x - 46x + 4x^2)
;
which is usually written
V(x) = x(4x^2 - 106x + 690)
;
multiply by the height
V(x) = 4x^3 - 106x^2 + 690x
RELATED QUESTIONS
an open-topped box is constructed from a rectangular piece of cardboard that is twice as... (answered by ikleyn,Theo)
A box with an open top is constructed from a rectangular piece of cardboard which is... (answered by ankor@dixie-net.com)
A box with an open top is to be constructed from a rectangular piece of cardboard with... (answered by ankor@dixie-net.com)
A box with an open top is to be constructed from a rectangular piece of cardboard with... (answered by ankor@dixie-net.com,nyc_function)
A box with an open top is to be constructed from a rectangular piece of a cardboard with... (answered by Cromlix)
A box with an open top is to be constructed from a rectangular piece of cardboard with... (answered by oberobic)
A box with an open top is to be constructed from a rectangular piece of cardboard with... (answered by checkley77)
A box with an open top is to be constructed from a rectangular piece of cardboard with... (answered by neatmath)
A rectangular box open at the top is to be from a rectangular piece of cardboard 3 inches (answered by Boreal)