Math Word Problem Help! function?

Question

A rectangular storage container measuring 2 feet by 2 feet by 3 feet is coated with a protective coating of plastic of uniform thickness.
A) Find the volume of the plastic V as a function of the thickness x (in feet) of the coating.
B) Find the thickness of the plastic coating to four decimal places if the volume of the shielding is 0.1 cubic feet.

Answer 1

A) I assume that the plastic in the inside the container against the walls

then Volume of plastic is

V = [ length*width*2 + length*height*2 + height*width*2 ] *x - correction

correction is for correcting the thickness of the plastic in the corners, and on the edges.
errrrrrrr it is not possible to have a uniform thickness in a rectangular container, how do you define the thickness in a corner ?

So you ignore the correction term by setting ity to zero

netto result :

V = [ length*width*2 + length*height*2 + height*width*2 ] *x - correction

B) 0.1 cubic feet

0.1 = [2*2 + 2*3 + 2*3]*x

solve this for x and you have the thing your teacher asked.
tell her that you ignored the constraint of uniform thickness in the corners

Answer 2

A. First, look for the total volume (the container plus the coating). The dimensions are 2+2x, 2+2x, and 3+2x (in feet, for each) because in each dimension the thickness of the coating has to be added twice (one for each side of the container). So, just multiply those 3 terms together, and then to get V you subtract the volume of the container, 12 cubic feet. That's:

V = (2+2x)(2+2x)(3+2x) - 12
(Leaving the rest to you - you might want to multiply those terms together to get a standard polynomial form.)

B. Now that you have V as a function of x, you just need to set V = 0.1 and solve for x. (Again, leaving the rest to you: this will be a cubic equation to solve.)