• Sep 4th 2012, 04:02 PM
allison
(Hi) Hi can someone help me solve this problem,please!!

A piece of cardboard measures 40 cm by 40 cm. An open-topped box is to be constructed by removing a square with side length of 8 cm from each corner and folding up the edges.
a) Find the surface area of the box. b) Find the volume of the box.
• Sep 4th 2012, 04:14 PM
pickslides
• Sep 4th 2012, 09:10 PM
Soroban
Hello, allison!

Quote:

A piece of cardboard measures 40 cm by 40 cm.
An open-topped box is to be constructed by removing a square with side length of 8 cm
from each corner and folding up the edges.

(a) Find the surface area of the box.

This is simple!

Its area is: $\displaystyle 40\times40 \,=\,1600 \text{ cm}^2.$

You remove four 8-by-8 squares.
So you remove: $\displaystyle 4 \times (8\cdot8) \,=\,256\text{ cm}^2$

So the surface area of the box must be: $\displaystyle 1600 - 256 \,=\,1344\text{ cm}^2.$

Quote:

(b) Find the volume of the box.

Did you make any sketches?

Code:

: - - -  40 - - - - :
- *---*-----------*---* -
: |///|          |///| 8
: *---* - - - - - *---* -
: |  :          :  | :
: |  :          :  | :
40 |  :          :  | 24
: |  :          :  | :
: |  :          :  | :
. : *---* - - - - - *---* -
: |///|          :///| 8
- *---*-----------*---* -
: 8 : -  24 - - : 8 :

The corner squares are removed
. . and the sides are folded upward on the dotted lines.

The open-top box looks like this:

Code:

*-----------*
/|          /|
/ * - - - - / *
/ /        / /
*-----------* / 24
8|          |/
*-----------*
24

I assume you can find the volume now . . .