New Question!!! (1 Viewer)

[sando]

A square sheet of metal is 16cm on each side. Squares of side xcm are cut from each corner. The sheet is then bent along the dotted lines to form an open box. What is the maximum volume of the box???

This is another question troublin me. Im sorry, i cant scan the pic up.

Thanks in advance, cos we r bound to get a question like this is exam

 

[Riviet]

Side length of the cross that is formed after cutting the squares of length x = 16-x-x = 16-2x. If we fold this up as stated in question, we form a rectangular prism with width and breadth of 16-2x and height x.

.'. V=x(16-2x)²
dV/dx=2x(16-2x)(-2) + (16-2x)²
=-4x(16-2x) + (16-2x)²
When dV/dx=0,
-4x(16-2x) + (16-2x)²=0
We observe that there is a common factor of 16-2x so we factorise it out:
(16-2x)(16-2x-4x)=0
(16-2x)(16-6x)=0
x=8, 8/3

Test both these values into V=x(16-2x)²,
When x=8, V=0
When x=8/3, V=8181/27 cm³

 

[sando]

thanks riviet, the problem i had was working out the height (x) lol