Asked by Annah
A box with an open top is been constructed from a piece of cardboard that is 4m wide by cutting a out a square from each side of that corner and bending up the side . Find the maximum volume
Answers
Answered by
oobleck
assuming the cardboard is square, then if the cut has length x,
v = x(4-2x)^2
max volume occurs when dv/dx=0, at x = 2/3
v = x(4-2x)^2
max volume occurs when dv/dx=0, at x = 2/3
Answered by
Reiny
Let the side of each cut-out square be x m
base = 4-2x by 4-2x
height = x
volume = x(4-2x)^2 = 16x - 16x^2 + 4x^3
d(volume)/dx = 16 - 32x + 12x^2
=0 for a max of volume
divide each term by 4
3x^2 - 8x + 4 = 0
solve for x
Make sure you reject the inadmissible root, remember 0 < x < 2 or else the dimensions
make no sense
base = 4-2x by 4-2x
height = x
volume = x(4-2x)^2 = 16x - 16x^2 + 4x^3
d(volume)/dx = 16 - 32x + 12x^2
=0 for a max of volume
divide each term by 4
3x^2 - 8x + 4 = 0
solve for x
Make sure you reject the inadmissible root, remember 0 < x < 2 or else the dimensions
make no sense
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.