Asked by Anonymous
A 5 cm by 5 cm square is cut from each corner of a rectangular piece of cardboard. The sides are folded up to make an open box with a maximum volume. If the perimeter of the base is 50 cm, what are the dimensions of the box?
Answers
Answered by
Steve
If the cardboard had dimensions x and y, then
2(x-10 + y-10) = 50
x+y = 45
Now, the volume is
v = 5(x-10)(y-10) = 5(x-10)(35-x) = -5(x^2-45x+350)
The vertex of this parabola (maximum volume) is at (45/2 , 3125/4)
2(x-10 + y-10) = 50
x+y = 45
Now, the volume is
v = 5(x-10)(y-10) = 5(x-10)(35-x) = -5(x^2-45x+350)
The vertex of this parabola (maximum volume) is at (45/2 , 3125/4)
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.