An open rectangular box is to be made from a piece of cardboard 8 inches wide and 8 inches long by cutting a square from each corner and bending the sides. Express the volume of the box as a function of the size x of the cutout.
2006-09-13 03:12:26 · 5 answers · asked by Jessie L 2 in Science & Mathematics ➔ Mathematics
Volume = length*width*height
If the box is made from an 8 x 8 square and cutting out an x by x square from each side, the length would be 8 - 2x (one x from each corner). The width would also be 8 - 2x and the height would be x. So, the volume of the box would be V = (8-2x)(8-2x)(x) which would simplify to 4x^3-32x^2+64x
2006-09-13 03:21:51 · answer #1 · answered by mathteacher 2 · 0⤊ 0⤋
V = x.(8-2x).(8-2x) = 4x.(4-x)^2
Assuming a side of each square is x units in length.
The base would then still be a square and the height is x units.
The top is given to be open.
V is the function of x for volume, it's easy to figure out how to get the above.
Remember a rough figure always helps and volume is
area x length
Hope this helps!
2006-09-13 11:28:56 · answer #2 · answered by yasiru89 6 · 0⤊ 0⤋
Ok, let's try this one,
Size with the 2 cuts x = 8-2x
The original area (8x8) is a square, so both sides are equal.
Volume = Area * height
V = (8-2x)^2*x
Good luck.
2006-09-13 10:17:05 · answer #3 · answered by alrivera_1 4 · 0⤊ 0⤋
let us cut a square of side X inch from the each corner of cardboard
then ,
remaining length=8-(2X) ( u r cutting X from both side)
remaining breadth=8-(2X) ( u r cutting X from both side)
height = X ( cut length)
then volume V= length*breadth* height
= (8-2X)*(8-2X)*X
( taking 2 common )
=4X*(4-X)^2 this is required function
2006-09-13 10:23:50 · answer #4 · answered by vicky 1 · 0⤊ 0⤋
V= HBW
V= X*8-2X*8-2X
2006-09-13 10:15:42 · answer #5 · answered by injureddancer 2 · 0⤊ 0⤋