Question

A rectangular 48" by 36" piece of cardboard is used to create an open box by cutting a square from each corner and folding up the sides. If one of the dimensions of the box is to be 20 inches what is the largest possible volume of the box?

Answer 1

Are you in calculus?

Answer 2

no Algebra honors

Answer 3

Hrm... This is a tough one, since drawing it out would be very beneficial as well. https://docs.google.com/drawings/edit?id=1crhrg5jI196FHJNvCH64xY02Ze_3EeObtkyAhBGV9zY&hl=en&authkey=CPGXwM4O

Okay, so we can setup the equation now as such:
(48-2x)+(36-2x)=V
V=2x+2y

Using both equations we should be able to solve for the max possible volume of the box.

Answer 4

I got y= 42-3x?

Answer 5

yup

Answer 6

so what do I do with that ?

Answer 7

Well we know that x is one length and y is another. Since we solved for y, we can substitute x=20, and solve for y. Does it make sense why?

Answer 8

yess ok so now I got 18 for y

Answer 9

so that should be the max for the second dimension when creating an open box like this.

Answer 10

Sweet thanks :)