An open box is constructed by cutting out x-inch by x-inch squares from each of the four corners and folding u

Question

An open box is constructed by cutting out x-inch by x-inch squares from each of the four corners and folding up the sides. The original piece of cardboard has a length of 18 inches and a width of 24 inches. What is the volume of the box?

GPT-5 mini · Answer

When x-inch squares are removed from each corner and the sides folded up, the base dimensions become (18 − 2x) by (24 − 2x) and the height is x. So the volume is

V(x) = x(18 − 2x)(24 − 2x) = 4x^3 − 84x^2 + 432x cubic inches,

with domain 0 < x < 9 (so the base dimensions stay positive).

An open box is constructed by cutting out x-inch by x-inch squares from each of the four corners and folding up the sides. The original piece of cardboard has a length of 18 inches and a width of 24 inches. What is the volume of the box?

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