Asked by Ally Mohamed

A closed cardboard box is designed to hold a volume of 3 288 cm . The length is 3 cm and the width x cm .Show that the total surface area 2 A cm is given by x A x 768 6 2   and find the dimensions of the box which will make A a minimum.
Answered by oobleck
I have no idea what "x A x 768 6 2" means, or what the two missing characters are, but if the height is h, then
3xh = 3288
A = 2(3x + (3+x)h) = 2(3x+(3+x) * 3288/(3x)) = 6x + 2192 + 6576/x
dA/dx = 6 - 6576/x^2 = 6(x^2-1096)/x^2
dA/dx=0 when x=2√274 and h = 2√274

max volume (min area) occurs when the box is as close as possible to a cube. Since we were given 3 as one dimension, then the other dimensions turn out to be a square.
Answered by Ally Mohamed
A closed cardboard box is designed to hold a volume of 288 cm^3 . The length is 3 cm and the width x cm .Show that the total surface area A cm^2 is given by A=6x^2+768/x and find the dimensions of the box which will make A a minimum. [8 Marks]
Answered by Norub
A closed cardboard box is designed to hold a volume of 3 288 cm . The length is 3 cm and the width x cm .Show that the total surface area 2 A cm is given by x A x 768 6 2   and find the dimensions of the box which will make A a minimum.
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