SOLUTION: Q: A rectangular open-topped box is to be constructed out of 20-inch-square sheets of thin cardboard by cutting x-inch squares out of each corner and bending the sides up as indica

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Q: A rectangular open-topped box is to be constructed out of 20-inch-square sheets of thin cardboard by cutting x-inch squares out of each corner and bending the sides up as indica      Log On


   

Question 1145023: Q: A rectangular open-topped box is to be constructed out of 20-inch-square sheets of thin cardboard by cutting x-inch squares out of each corner and bending the sides up as indicated in the figure. Express each of the following quantities as a polynomial in both factored and expanded form. (A) The area of cardboard after the corners have been removed. (B) The volume of the box.
A: I know area = 20^2. I'm guessing the 4 cut squares would be 4x^2? So would the area, before factorization, be just +20%5E2+-+4x%5E2+? And factorization would be +400+-+4x%5E2+=+4%28100+-+x%5E2%29+?
While I kind of understood area, I'm lost on volume. I know the equation for volume is length x width x height, but I'm not sure how to apply that here.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
x, the edge cut out at each corner, also becomes the box height.

Volume, x%2820-x%29%5E2, the factored form.

The area of the bottom is %2820-x%29%2820-x%29.