Posted by Layla on Saturday, October 9, 2010 at 8:04pm.
A box with a square base and an open top is constructed from 5400 cm^2 of cardboard. Find the dimensions of the largest possible box.
I know the answer is :
base lenght  42.4 cm
height 21.2 cm
please help me, thank you so much :)

PreCal  bobpursley, Saturday, October 9, 2010 at 9:17pm
It depends on the shape of the 5400cm^2 cardboard.
If it is square, it is sqrt5400 or 73.4cm to a side.
Now set it down, call the sides s, and the height h.
You have to cut out h^2 from each of the four corners.
Area=b^2 h
but 2h+b=73.4 or h=(73.4b)/2
Area=b^2(73.4b)/2
dArea/db= 2b(73.4b)/2 b^2/2=0
solve for b
Then use that to go back and solve for h.

PreCal  Reiny, Saturday, October 9, 2010 at 9:45pm
If this is the typical questions, identical squares are to be cut out of each of the corners of the cardboard, and then the sides folded up to form the box.
Let each side of the cutout be x cm
so each side of the base of the box will be √5400  2x
volume of box
= x(√54002x)(√54002x)
= 5400x4√5400x^2 + 4x^3
d(volume)/dx = 5400  8√5400x + 12x^2 = 0 for a max of volume
x^2  20√6 + 450 = 0
using the quadratic formula
x = (20√6 ± √(2400 4(1)(450))/2
= (20√6 ± √600)/2
= 36.74 or 12.25
The first answer gives us a volume of zero, the minimum, and the second gives us the maximum value
height = 12.25
base = √54002x = 48.99
Answer This Question
Related Questions
 Pre Cal  find the surface area of a box of hieght h whose base dimensions are p...
 PreCal  A square sheet of cardboard 18 inches is made into an open box (there ...
 calculus  A rectangular box is to be constructed from two different materials. ...
 pre calc  A cardboard box has a square base and a square top. The height of the...
 Calculus  A cardboard box of 32in^3 volume with a square base and open top is ...
 Calculus 1Optimization  A box with a square base and open top must have a ...
 calculus  This is problem 16 Section 4.6 page 246. A closed box with square ...
 MATH  A box with an open top has vertical sides, a square bottom, and a volume ...
 Physics  An open box with a square base (see figure) is to be constructed from ...
 CALC  An open box is to be constructed so that the length of the base is 4 ...
More Related Questions