The following exercises are geometric in nature and lead to polynomial models. Solve each problem.

A rectangular piece of cardboard measuring 12 in. by 18 in. is to be made into a box with an open top by cutting equal-size squares from each corner and folding up the sides. Let x represent the length of a side of each such square in inches. Give approximations to the nearest hundredth.

(a) Give the restrictions on x.

(b) Determine a function V that gives the volume of the box as a function of x.

(c) For what value of x will the volume be a maximum? What is this maximum volume?

(d) For what values of x will the volume be greater than 80 in.³?

Transcribed Image Text:

18 in. х х х х 12 in. х х |х х