If a total of 1700 square centimeters of material is to be used to make a box with a square base and open top, find the largest possible volume of such a box?

Step-by-step explanation:

Here we have to find the value for in order to have the maximum volume () of the box, where the area of the box is given by:

(1)

And the volume:

(2)

Isolating from (1):

(3)

Substituting (3) in (2):

(4)

So, we have to derive this expression, then make it equal to zero and solve the equation to find the critical point:

(5)

Making :

(6)

The critical point is:

(7)

This means the maximum Volume is when . Now with this value we can find :

(8)

Hence:

(9) This is the maximum volume of the box

6(h+1)/2=a

a=area

step-by-step explanation:

its the same thing as a square or rectangle but after multiplying two sides you need to divide it by two.