Question

An open box will be made from a rectangular piece of cardboard that is 8 in. by 10 in. The box will be cut on the dashed red lines, removing the corners, and then folded up on the dotted lines. The box needs to have the MAXIMUM volume possible. How long should the cuts be?
A. 1.5 inches
B. 5.8 inches
C. 52 inches
D. 80 inches

Answer 1

if x is the length of a dashed line then the volume of the box is

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

Answer 2

This needs to be a maximum
Find dV/dx and equate to zero
Then solve for x
One of the roots will give the maximum volume

Answer 3

Oh Are you familiar with calculus? Differentiation?
If not we need to solve it another way.

Answer 4

I don't know how to do it that way. I'm taking tenth grade analytical geometry/ advanced algebra.

Answer 5

I made a mistake in my first post
V = x(10-2x)(8 - 2x)

Answer 6

- i missed out the height of the box (x)

Answer 7

One way to do this would be to draw the graph of the function manually or using graphing software.

Answer 8

Why would you need to graph?

Answer 9

i cant think of another way other than using calculus.
Oh - you could do it by plugging in each given value in the choices to see which gives the maximum

Answer 10

Ok ill try that thanks.

Answer 11

Chances are that you can only estimate the maximum if the only resource you have to work with is a graph. Using a graphing utility to produce an accurate graph will simplify your estimation.