Question

Kenard takes a square piece of cardboard and cuts 4 in. by 4 in. squares out of each corner. He folds the sides up to make a box without a top. What equation can Kenard use to determine the volume of the box, where x is the side length of the original piece of cardboard

Answer 1

4x² - 64x + 256

I hope this helps. (:

Answer 2

`4x^2-64x+256`

Explanation:

Since original square has sides x,

when we cut 4 units from all the 4 sides the box will have height of 4 units.

Length of the box = side of square - 2 times square side cut

= x-2(4) = x-8

Similarly width of the box also would be

x-8

Hence volume of the box = lwh

= length x widthx height

Now substitute for each in terms of x

Volume =
`(x-8)(x-8)(4)\\=4x^2-64x+256`