Question

If 900 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

Answer 1

Find the max volume.
Volume formula=length and width and height
in this case we'll call the base x and heigh h, so volume of box=(x^2)h
Find the area of the box first since the only information the problem tells us is that we're given 900sq cm of material. so..
Area of the box is 900 made up of =Area of the base + Area of the 4 sides
900=(x^2)+ 4xh solve for h now
900-x^2=4xh
(900-x^2)/(4x)=h
(225/x) - (x/4) = h
now that you've solved for h, you can plug that equation into the original volume equation. after that, you would want to differentiate it in order to find the critical numbers. by doing so, you can find the max volume.

Answer 2

got it?