A box with no top is being made out of a 20 cm by 30 cm piece of cardboard

Question

1. A box with no top is being made out of a 20 cm by 30 cm piece of cardboard by cutting equal squares of side length x from the corners and folding up the sides. Determine an algebraic model for the volume of the box. Use your model to determine the volume if the side length of each square is 6 cm.

Answer 1

Definitely draw a picture to help visualize the problem, or better yet, get a piece of paper and cut out the corners yourself to create a box! This will be extremely helpful to grasp the problem.

Recall the formula for the volume of a box (ie, a rectangular prism) V = lwh, where l: length, w:width, and h:height.

You are cutting out squares of side length x from the original 20cm by 30cm slab of cardboard. How does this affect the length and width of the cardboard. If you crafted your own box, what was the height? It relates to the squares you cut out.