Chris makes an open-topped box from a 30cm by 30cm piece of cardboard by cuting out equal squares from the corners and folding up the flaps to make the sides. What are the dimensions of each square, to the nearest hundreth of a centimetre, so that the volume of the resulting box is 1000cm^3? Thanks !

Question

mathmale · Answer

How about coming up with the basic formula for the volume of a rectangular box?
Next, assume that the length and width of the box are the same, since it's to be made from a square of cardboard.
Draw a picture showing each of the four corners gone (cut out).
Write an expression for the length of each side of the resulting bottom of the box.
Next, write an expression for the area of the bottom of the box.
Last, write an expression for the volume of the box.  Remember:  volume = base * height.

mathmale · Answer

Set this volume equal to 1000 cm^3 and solve for x.  Voila!