Posted by irma on Sunday, May 12, 2013 at 1:38am.
a square sheet of tin 30cm on a side is to be used to make an open  top box by cutting a small square of tin from each corner and bending up the sides. how large should be the square cut from each corner to make the box's volume as large as possible

math  Reiny, Sunday, May 12, 2013 at 6:43am
let the size of the cutout square be x cm by x cm
then after bending,
the base of the box will be 302x by 302x and x cm high
Volume = x(302x)^2
= x(900  120x + 4x^2)
= 4x^3  120x^2 + 900x
d(Volume)/dx = 12x^2  240x + 900
= 0 for a max/min of Volume
12x^2  240x + 900 = 0
x^2  20x + 75 = 0
(x5)(x15) = 0
x = 5 or x = 15 , (clearly x = 15 yields a minimum volume of 0)
So the size of the cut should be squares of 5 cm by 5 cm.
Answer This Question
Related Questions
 algebra  An open box is to be constructed from a rectangular sheet of tin 5 ...
 Calculus  an open top box is to be made by cutting congruent squares of side ...
 Algebra  An open box is to be constructed from a rectangular sheet of tin 3 ...
 inermediate algebra  A box with no top is to be made by cutting a 2inch square...
 Calculus (Optimization)  A rectangular piece of cardboard, 8 inches by 14 ...
 math,algebra  an open box is to be made by cutting small congruent squares from...
 math  application of derivatives: an open box is to be made by cutting small ...
 caculas  an open box is to be made by cutting small congruent squares from ...
 math  it is required to make an open box of gregreatest possible volume from a ...
 maths  a square piece of tin 31cm and20cm is to be made into a box without top,...
More Related Questions