Question

The frame for a rectangular box is to be constructed from 44 feet of a thin metal rod. The metal rod is to be cut into pieces such that the bottom of the box is a square with edge length x. Express the volume, V, of the box as a function of x.

Answer 1

V = x^2 * h
also total length of frame
= 44 = 4x + 4x + 4h
44 = 8x + 4h
express h in terms of x using above equation and substitute for h in the formula for V

Answer 2

thank you))

Answer 3

yw

Answer 4

can you continue from the above?

Answer 5

I guess...but could you please finish it?

Answer 6

the square length is x



there is 8x in the frame

height = (44 - 8x)/4 4 edges of the same height

height = 11 - 2x

the volume is

\[V = x^2 \times (11 - 2x) = 11x^2 - 2x^3\]