An open-top box is to be constructed from a 6 in by 2 in rectangular sheet of tin by cutting out squares of equal size at each corner, then folding up the resulting flaps. Let x denote the length of the side of each cut-out square. What is the volume?

2 Answers
Jun 17, 2016

Answer:

Volume#=x^3-16x^2+12x#

Explanation:

Height of box: #=x#
Length of box: #=6-2x#
Width of box: #=2-2x#

Volume of box:
#x*(6-2x)(2-2x)#
#color(white)("XXX")=x*(12-16x+4x^2)#
#color(white)("XXX")=x^3-16x^2+12x#

Jun 17, 2016

Answer:

Volume of open-top box would be #4x^3-16x^2+12x#

Explanation:

As #x# is the length of the side of each cut out square, the height of the open=top box will be #x#.

Its length will be #(6-2x)#

and width would be #(2-2x)#

Hence volume would be

#x(6-2x)(2-2x)#

= #x(12-12x-4x+4x^2)#

= #x(12-16x+4x^2)#

= #12x-16x^2+4x^3#

or #4x^3-16x^2+12x#