Question

The Brilliant Butler Company wishes to design a serving tray that will contain the most fluids in case of a spill. The serving tray is designed from a 6- by 16-inch piece of tin by cutting identical squares from the corners and folding up the flaps as shown in the figure below, where a = 6 and b = 16.

Length b-2x

Height a-2x

(a) Write a function V(x) that gives the volume of the serving tray in terms of its height x.

Write an open interval for the domain of the function. (Enter your answer using interval notation.)

(b) Determine the height, length, and width of the tray that maximizes the volume.

height	in
length	in   (longer side)
width	in (shorter side)

c) What is the maximum volume? (Round your answer to two decimal places.)

V = _____in^3

Answer 1