Question – 4: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 5 in. by 10 in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure.
(a) Express the volume V of the box as a function of x, then determine the range and the domain of this function.
(b) Express the surface area S of the box as a function of x, then determine the range and the domain of this function.
(c) Find the value of x that gives the largest volume of the box.
2007-11-10 02:58:57 · 2 answers · asked by yamisfy 1 in Science & Mathematics ➔ Mathematics
Volume = (10-2x)(5-2x)x = 4x^3-30x^2 +50x
in order for the volume to be positive, 0
Surface area = 50 -4x^2
domain (-sqrt(12.5, sqrt(12.5)) in order for area to be positive
Range y=< 50
Max volume occurs when x = {15-5sqrt(3)}/6 = 1.0566...
2007-11-10 03:51:52 · answer #1 · answered by ironduke8159 7 · 0⤊ 0⤋
a) V = x(10-2x)(5-2x)
b) S = 10*5 - x^2
c) Solving V' = 0 for x gives you the answer: Vmax = 24.056 in^3
2007-11-10 11:32:22 · answer #2 · answered by sahsjing 7 · 0⤊ 0⤋