Maximum possible volume, given1200cm^2 of material, square base and open top

Submitted by deep076 on

I need help

Jhun Vert Thu, 04/20/2017 - 06:29

Our moderator lock this post for lack of data. The information actually is complete, we think the given 1200 cm3 is supposed to be a total surface area, the correct unit should be cm2.

We revised the problem and open it for commenting.

esmilitar Fri, 04/21/2017 - 05:52

Maximum possible volume, given1200cm^2 of material, square base and open top
Volume = x2y
Surface Area = 1200 = 4x2 + xy =⇒ y =(1200 − 4x2)/x
v = x2y
v(x) = x2(1200 − 4x2)/x

v(x) = x(1200 − 4x2)
v'(x) = (1200 − 4x2) + x(−8x)
0 = 1200 − 12x2
0 = 100 − x2
x = ±10
v"(x)=-24x
v"(10)0
There is a maximum when x = 10 and y = 12
The largest possible volume of the box is 1200 cm3

Jhun Vert Fri, 04/21/2017 - 08:42

Hello po sir, I think your total surface area was interchanged. Since the base is square and open top, if the dimensions of the square base is x by x and the depth is y then the total surface area should be: x2 + 4xy = 1200

This problem is one of the common variable relationships of maxima and minima. This one needs no differentiation if we can familiarized the result. The result of this is always x = 2y.

Of course, doing the differentiation cannot be discounted. We really need it specially if the problem is twisted in another way so that the x = 2y is no longer applicable.

This problem is actually common to engineering board exams, it is encouraged to memorized the variable relationship rather than do the differentiation process to save considerable amount of time.

My answer to this problem is 4,000 cc.