Answer:
[tex]V = x^3-24x^2+35x[/tex]
Step-by-step explanation:
Jack makes a cuboid. If the length is l, the width is w and the height is h, then its volume is
[tex]V = lwh[/tex]
The height is determined by the side of the square cut out of each corner.
[tex]h = x[/tex]
Along the length of the width, the length of two sides of the square are cut.
[tex]l = 7 - 2x[/tex]
[tex]w = 5 - 2x[/tex]
[tex]V = lwh = (7-2x)(5-2x)(x)[/tex]
[tex]V = x(35-24x+4x^2) = x(x^2-24x+35) = x^3-24x^2+35x[/tex]
Answer:
Step-by-step explanation:
Given:
Dimensions of rectangle cardboard:
Length, l = 7 inches
Width, b = 5 inches
if the square of sides x inches is cut from each corner of the rectangular cardboard and folded to make a tray, therefore:
Length of the tray = length of cardboard - 2 (side of the square )
= 7 - (2 × x)
= 7 - 2x inches
Width of the tray = width of cardboard - 2(side of square)
= 5 - (2 × x)
= 5 - 2x inches
height of tray = cut sides of square
= x inches
volume of tray = Length × width × height
= (7 - 2x) × (5 - 2x) × x
Volume of tray = 35x - 10x^2 - 14x^2 + 4x^3
Simplifying further,
= (35x - 24x^2 + 4x^3) cubic inches
