Volume of a Box A rectangular piece of cardboard measuring 12 in. by 18 in. is to be made into a…

 

Volume of a Box 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.

 

Volume of a Box A rectangular piece of cardboard measuring 12 in. by 18 in. is to be made into a box...-1

(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 maximumvolume? (Hint: Use the function of a graphing calculator that allows us to determinea maximum point within a given interval.)

(d) For what values of x will the volume be greater than 80 Volume of a Box A rectangular piece of cardboard measuring 12 in. by 18 in. is to be made into a box...-2

 

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