Arlan needs to create a box from a piece of cardboard. The dimensions of his cardboard are 10 inches by 8 inches. He must cut a square from each corner of the cardboard, in order to form a box. What size square should he cut from each corner, in order to create a box with the largest possible volume?

A.0.5 inches

B. 1 inch

C. 1.5 inches

D. 2 inches
I think its C ?

3 answers

L = 10 - 2x
w = 8 - 2 x

v = L * w * x

v = (10-2x)(8-2x)x
v = (80 - 36 x + 4 x^2)x
v = 4 x^3 - 36 x^2 + 80 x
do you do calculus?
if so the
min or max when dv/dx = 0
0 = 12 x^2 -72 x + 80
0 = 3 x^2 - 18 x + 20
x = 3 +/- (1/3)sqrt 21
= 3 +/- 1.52
the plus sign is too big a width
so
3 - 1.52
is 1.5 close enough

no , So its D ? 2 inches

Nope, C 1.5 inches