SOLUTION: A square piece of cardboard is to be formed into a pizza box. The box is formed by cutting 2-inch square corners from the cardboard and folding them up. If the volume of the box is

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A square piece of cardboard is to be formed into a pizza box. The box is formed by cutting 2-inch square corners from the cardboard and folding them up. If the volume of the box is      Log On


   

Question 144121: A square piece of cardboard is to be formed into a pizza box. The box is formed by cutting 2-inch square corners from the cardboard and folding them up. If the volume of the box is 512 in^3, what are the dimensions of the cardboard?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
The side of the cardboard square: x
The length and width of the box: x - 4 (because you need to subtract 2 inches from each side)
The height of the box: 2

Volume of the box %28x-4%29%28x-4%29%2A2=512

Multiply the binomial and divide both sides by 2:
x%5E2-8x%2B16=256

x%5E2-8x-240=0

%28x%2B12%29%28x-20%29=0

x=-12 or x=20. Exclude the negative root as extraneous and not meaningful since we are looking for a positive measure of length. The original cardboard was then 20 inches by 20 inches.

Check:
Cut out 2 inch squares from the corners of a 20 X 20 piece of cardboard and then fold up the sides, making a 16 by 16 by 2 box. 16%2A16%2A2=512 Checks.