A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 inches by 20 inches by cutting out equal squares of side x at each corner and then folding up the sides.
(a) Find a function that models the volume V of the box in terms of x.
V =
(b) Find the values of x for which the volume is greater than 200 in3. Give your answers correct to 3 decimal places. Give as an inequality
(c) Find the largest volume that such a box can have. Give your answers correct to 3 decimal places.
2007-09-19 09:43:52 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
sfroggy, i can get as far as you, that parts easy, but you have to get the answer so there are no variables.
2007-09-19 09:54:40 · update #1
height = x
length = 20 - 2x
width = 12 - 2x
V > lwh
200 > (20 - 2x)(12 - 2x)(x)
2007-09-19 09:51:52 · answer #1 · answered by sfroggy5 6 · 0⤊ 0⤋
(a) V=(x)(12-2x)(20-2x) (you'll have to expand that for yourself)
(b) set V=200, or 200=(x)(12-2x)(20-2x), solve for x, make a number line, test one value within each region bound by given x's.
(c) what class are you in? if calculus, take the derivative of the V equation up there, find the zeros of the derivative equation, test each one in V, find the maximum that way... this is probably confusing, i wish i could draw a picture.
2007-09-20 04:20:30 · answer #2 · answered by brad k 2 · 0⤊ 0⤋
x = size of side of square corner cut out
Then x = height of box
12-2x = width of box
20-2x = length of box
V = x(12-x)(20-x) = x^3-32x^2+240x
V larger than 200 in^3 when .950
max at x= 4.86666 = 525.362 in^3
2007-09-19 10:38:14 · answer #3 · answered by ironduke8159 7 · 0⤊ 0⤋