Algebra/geometry problem solving Carboard problem

Question

you need to build a box from an 8 inch by 10 inch piece of cardboard. to do this, you cut out squares of length x from the four corners of the box in order to golf the sides up..

find the expression that gives the volume of the box V in terms of the height of the box X

what are the possible volumes that the box can have? in other words, pick several sensible values of x and evaluate your expressions for each.

Answer 1

If you're having a hard time understanding, try taking a single sheet of paper, and trying it out!

It might help to just pick a length for x.. like 2 inches. So then cut a 2 x 2 box out of each corner..

Fold the corners and find the volume.. 8-2 = 6 and 10-2 = 8 and the height is 2... so 2 x 6 x 8 = volume.. get it?

If you take the formula for volume of a cube V = l x w x h, and rewrite it with your information, you should be able to find your answers.

Answer 2

Algebra/geometry problem solving Carboard problem

you need to build a box from an 8 inch by 10 inch piece of cardboard. to do this, you cut out squares of length x from the four corners of the box in order to golf the sides up..

find the expression that gives the volume of the box V in terms of the height of the box X

what are the possible volumes that the box can have? in other words, pick several sensible values of x and evaluate your expressions for each.

First, draw a picture (however rough).

XOOOOOOOOX

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

XOOOOOOOOX

" expression that gives the volume of the box V in terms of the height of the box X" is

V = length*width*height

V = (10-2x)(8-2x)*x

V = (60 - 20x -12x + 4x²)*x [use F-O-I-L]

V = (4x² -32x + 60)*x [re-order]

V = 4x³ - 32x² + 60x [distribute]

Now, some points (x,V):

x V

1 32

2 24

3 0 [note: This means folding the cardboard in half !!]