An open top cake tin is to be made by cutting a square (xcm by xcm) from each corner.

Develop a conjecture about the relationship between x (the cut to be made for the square) and the length of each side of the rectangle such that the cake tin has a maximum volume.

The sides of the rectangle are in a ratio r:s. Consider a rectangle where one side is twice the length of the other (i.e. 2:1). Find the value of x that gives the maximum volume for the cake tin. Repeat this process for rectangular tinplates with sides in at least two other ratios. Please help!!!!!

Question

An open top cake tin is to be made by cutting a square (xcm by xcm) from each corner.
 
Develop a conjecture about the relationship between x (the cut to be made for the square) and the length of each side of the rectangle such that the cake tin has a maximum volume. 

The sides of the rectangle are in a ratio r:s. Consider a rectangle where one side is twice the length of the other (i.e. 2:1). Find the value of x that gives the maximum volume for the cake tin. Repeat this process for rectangular tinplates with sides in at least two other ratios. Please help!!!!!

mathmale · Answer

I'd suggest you sketch a rectangle of length L and width W.  Remembering that you have to cut out squares from the four corners, and letting the side of such a square be x, how would you write an expression for the volumne of the resulting container?

devebr · Answer

|dw:1476310655650:dw|