Cube-shaped boxes will be loaded into the cargo hold of a truck. The cargo hold of the truck is in the shape of a rectangular prism. The edges of each box measure 2.50 feet and the dimensions of the cargo hold are 7.50 feet by 15.00 feet by 7.50 feet. What is the volume, in cubic feet, of each box? (Big box volume) and (small box volume)

Solve each problem. Volume of a Box A piece of sheet metal is 2.5 times as long as it is wide. It is to be made into a box with an open top by cutting 3 -inch squares from each corner and folding up the sides, as shown at the top of the next page. Let x

represent the width of the original piece of sheet metal. (a) Represent the length of the original piece of sheet metal in terms of x.

(b) What are the restrictions on x?

(c) Determine a function V

that represents the volume of the box in terms of x

(d) For what values of x

(that is, original widths) will the volume of the box be between 600 and 800 cubic inches? Determine the answer graphically, and give values to the nearest tenth of an inch