# Thread: Need help with a basic problem :)

1. ## Need help with a basic problem :)

It may be basic, but I'm just going into Calculus now, so I'm kind of hesitant on where to start.

Question:
An open box is to be made from cutting squares of side s from each corner of a piece of cardboard 25" by 30"
a) Write an expressions for the volume, V(s), in terms of s
b) Draw a graph of V(s)
c) What domain and range make sense in this problem situation?
d) Find the value of s that will give the max volume, and what is the max volume?
e) What value of s will give a volume of 1225 cubic units?

I just need to know how to start it, because I'm just not sure if I should use surface area, area, or derivative or whatnot.

2. Originally Posted by glamchic
It may be basic, but I'm just going into Calculus now, so I'm kind of hesitant on where to start.

Question:
An open box is to be made from cutting squares of side s from each corner of a piece of cardboard 25" by 30"
a) Write an expressions for the volume, V(s), in terms of s
b) Draw a graph of V(s)
c) What domain and range make sense in this problem situation?
d) Find the value of s that will give the max volume, and what is the max volume?
e) What value of s will give a volume of 1225 cubic units?

I just need to know how to start it, because I'm just not sure if I should use surface area, area, or derivative or whatnot.
Start by writing the expression for the volume V in terms of s. The height
of the box will be s, its length 30-2s, and its depth 25-2s. Drawing a
picture will also help.

RonL

3. Hello, glamchic!

An open box is to be made from cutting squares of side $s$
from each corner of a piece of cardboard 25" by 30"
Some instructions were left out here, right?

a) Write an expressions for the volume, $V(s)$, in terms of s
b) Draw a graph of $V(s)$
c) What domain and range make sense in this problem situation?
d) Find the value of $s$ that will give the max volume, and what is the max volume?
e) What value of s will give a volume of 1225 cubic units?

I just need to know how to start it, because I'm just not sure if I should use surface area,
area, or derivative or whatnot.
Of course you aren't sure . . . you don't understand what it's asking, do you?

This is the cardboard with the squares to be removed from each corner.
Code:
      : . . . . 30  . . . :
- *---+-----------+---*  -
. |:::|           |:::|  s
. + - * - - - - - * - +  -
. |   :           :   |  .
25 |   :           :   | 25-2s
. |   :           :   |  .
. + - * - - - - - * - +  -
. |:::|           |:::|  s
- *---+-----------+---*  -
: s : . 30-2s . : s :

Then the four "flaps" are folded up to form an open-top box.
Code:
            *-------------*
/ |           / |
/   |         /   | s
*-------------*     |
|             |     *
s |             |   /25-2s
|             | /
* - - - - - - *
30-2s

The volume of a box is: . $V\;=\;L \times W \times H$

So we have: . $V\;=\;(30-2s_)25-2s)s$

Therefore: . $V(s)\;=\;750s - 110s^2 + 4s^3$

Can you continue from here?

4. ## Thanks!

Yess!! Thanks for all your help, you guys! And guess what, I was on the right track! I just doubt myself too much. Thanks again!