Asked by PHILLIP
A square sheet of cardboard has sides 18cm. Four equal portions are cut away from the corner and discard. The sides are then twiced up to form a restangular box. What are the dimension of the box formed that will have max volume?
Answers
Answered by
Damon
L = 18-2x
w = 18-2x
h = x
V = x(18-2x)^2
dV/dx = 0 for max or min
0 = x (2)(18-2x)(-2) + 1 (18-2x)^2
0 = -4x (18-2x) + 324 - 72 x + 4 x^2
0 = -72 x + 8 x^2 + 324 -72 x + 4 x^2
0 = 12 x^2 - 144 x + 324
0 = x^2 - 12 x + 27
0 = (x-3)(x-9)
x = 3 or 9
but 9 will not work (is V=0) so use 3
w = 18-2x
h = x
V = x(18-2x)^2
dV/dx = 0 for max or min
0 = x (2)(18-2x)(-2) + 1 (18-2x)^2
0 = -4x (18-2x) + 324 - 72 x + 4 x^2
0 = -72 x + 8 x^2 + 324 -72 x + 4 x^2
0 = 12 x^2 - 144 x + 324
0 = x^2 - 12 x + 27
0 = (x-3)(x-9)
x = 3 or 9
but 9 will not work (is V=0) so use 3
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.