Question

Consider an open-top box constructed from an 8.5 × 11 inch piece of paper by cutting out squares of
equal size at the corners, then folding up the resulting flaps. Denote by x the side-length of each cut-out
square.
a) Draw a picture of this construction, and find a formula for the volume V of the box as a function
of x.
b) State the domain of V (x). (The domain is not all real numbers!)
c) Scaling appropriately, use your calculator to sketch the graph of V .

Answer 1

width = 8.5-2x
length = 11 - 2x
height = x

V = x(8.5-2x)(11-2x)
domain: 0 < x < 4.25