A piece of rectangular cardboard has dimensions 27\" by 18\". You are to cut squ

Question

A piece of rectangular cardboard has dimensions 27" by 18". You are to cut squares from each corner and bend up the sides to form a box (with no lid). Write a model to represent the volume of the box. Find all possible cut-out sizes so that the volume of the box is 715 cubic inches. What is the domain? A piece of rectangular cardboard has dimensions 27" by 18". You are to cut squares from each corner and bend up the sides to form a box (with no lid). Write a model to represent the volume of the box. Find all possible cut-out sizes so that the volume of the box is 715 cubic inches. What is the domain?

Explanation / Answer

length = 27''

width = 18''

side of square= x

V = x* ( 27-2x)(18-2x)

715 = 4x^3-90x^2+486x

4x^3-90x^2+486x - 715 =0

(2x-5)(2x^2-40x+143) = 0

(2x-5)( x - 15.3)(x +4.66) = 0

x = 5/2 , 15.3 , -4.66

[-4.66, 15.3]

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