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 :)
- Pre-Cal - 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.
but 2h+b=73.4 or h=(73.4-b)/2
dArea/db= 2b(73.4-b)/2 -b^2/2=0
solve for b
Then use that to go back and solve for h.
- Pre-Cal - 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
= 5400x-4√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 = √5400-2x = 48.99
Answer this Question
- Pre Cal - find the surface area of a box of hieght h whose base dimensions are p...
- calculus - A rectangular box is to be constructed from two different materials. ...
- Calculus - A cardboard box of 32in^3 volume with a square base and open top is ...
- Pre-calc - A cardboard box with an open top and a square bottom is to have a ...
- Calculus -- HELP! - If 1200 square centimeters of material is available to make ...
- math - If 507 square centimeters of material is available to make a box with a ...
- CALC - If 1700 square centimeters of material is available to make a box with a ...
- calculus - 7. A cardboard box manufacturer wishes to make open boxes from ...
- math - A cardboard box manufacturer wishes to make open boxes from rectangular ...
- Math - An open-topped box is constructed from a piece of cardboard with a length...