If 300 cm2 of material is available to make a box with a square base and an open top, find the maximum volume of the box in cubic centimeters. answer to the nearest cubic centimeter without commas.

Maximum volume of box is 500 cubic centimeters.

Step-by-step explaination:

Given 300 of material available to make a box with a square base and an open top that means given area of box is 300 . Now, we have to find the maximum volume of box.

Now, area of box with square box and open top = area square base + 4ab

                                                     =

⇒ = 300

⇒    →  (1)

Now, Volume of box  i.e

Using eq (1),                    

                                                  =

To find maximum volume differentiate above eq w.r.t aand then and equate to 0, we get

⇒        

⇒           ⇒ a=10

⇒                

hence, Volume=100(5)=500