Posted by annie on Wednesday, March 27, 2013 at 11:42am.
An open box is made from a rectangular piece of cardboard measuring 16 cm by 10cm. Four equal squares are to be cut from each corner and flaps folded up.
Find the length of the side of the square which makes the volume of the box as large as possible.
Find the largest volume

math  Steve, Wednesday, March 27, 2013 at 11:50am
the base of the box is 162x by 102x, and the height is x
v = x(162x)(102x)
v'= 4(x2)(3x20)
20/3 >5, so it's too large
so, max volume occurs when x=2
The box is 6x12x2 with volume 144

math  annie, Wednesday, March 27, 2013 at 11:58am
@steve
Why is the base of the box 162x by 102x
(where did the 2x come from?)

math  Steve, Wednesday, March 27, 2013 at 12:17pm
because x was cut off each corner. Draw a diagram, and you will see that when the corners are turned up, the sides have 2x cut off.
Answer This Question
Related Questions
 Algebra  Identical squares are cut off from each corner of a rectangular piece ...
 Calculus  Squares with sides of length x are cut out of each corner of a ...
 Calculus  Squares with sides of length x are cut out of each corner of a ...
 math 12  $identical\:squares\:are\:cut\:from\:each\:corner\:of\:a\:rectangular...
 algebra  An opentop box is to be constructed from a 6 foot by 8 foot ...
 Math  A Candy box is made from a piece of cardboard that meaasures 11 by 7 ...
 math  The length of a rectangular piece of cardboard is three more than twice ...
 algebra  A rectangular piece of cardboard is 2 units longer than it is wide? ...
 Algebra 104  1. A square piece of cardboard measuring 60 inches on a side is ...
 math  An opentop box is to be constructed from a 6 foot by 8 foot rectangular ...
More Related Questions