# Calculus- volume of a square based object

• May 27th 2009, 07:05 AM
mathkid
Calculus- volume of a square based object
hey guys, i am real stuck with this question and would like some help!
The question is:
An open top box is to be made from a square sheetof metal with a side of 12cm , by cutting a square from each corner and bending the sides up along the dashed lines.
Find the dimensions of the cut out that will result in a box of the greatest volume.
Sorry I dont have the drawing, but it is a square with 1 rectangle on each side.
Thanks
• May 27th 2009, 07:25 AM
Amer
since the sheet is square you should cut a squares from the corners not rectangles because if you cut rectangle the hight of the box will be change from side to side

let the square side be x so the volume of the box equal

(12-2x)(12-2x)x=v
v=4x^3-48x^2+144x
dv/dx=12x^2+-96x+144
0=12(x^2-8x+12)
12(x-2)(x-6)=0
x=2 or x=6
substitute 2 and 6
v(6)=0
v(2)=128

Attachment 11646
Attachment 11647
• May 27th 2009, 06:08 PM
mathkid
thanks heaps mate, really helped (Rofl)