Question

Consider the same rectangle of the preceding 8 units. Squares of x by x units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume of the box as a polynomial function in terms of x problem. Squares of 2x by 2x units are cut out of each corner. Express the volume of the box as a polynomial in terms of x.

Answer 1

Answer:

V(x) = l*w*x  - 2*l*x² - 2*w*x² + 4*x³

Step-by-step explanation:

The volume of any box is:

a * b * h       where a is the length, b is the wide and h is the height

Assuming we have cardboard of dimensions: l * w

l - 2*x  will be length  of the box and  

w - 2*x will be wide of the box

h  =  x the height, then:

V(x) = ( l  -  2*x  ) *  (  w  -  2*x ) * x

V(x) = [ ( l*w - 2*l*x - 2*w*x + 4*x² ] * x

V(x) = l*w*x  - 2*l*x² - 2*w*x² + 4*x³