110. A sphere has radius 2 inches. A cube is fit perfectly inside of the ball such that all 8 corners of the cube touch the sphere. What are the dimensions of the cube? 111. A typical cereal box is 2 inches by 6 inches by 12 inches. Suppose a company wants to change the shape of the cereal box so that it uses less cardboard, and is thus more environmentally friendly. Find a "reasonable" new size for the cereal box that minimizes the amount of cardboard used while still maintaining the volume of the original box. Explain why your solution is reasonable. 112. In this problem use the metric system. Suppose an aluminum can must hold 440 cubic centimeters (about a typical soda can). A company that sells soft drinks wants to design a can so that it minimizes the amount of aluminum used. What are the dimensions of a can (in the shape of a cylinder) that minimizes the amount of aluminum used, while still holding 440 cubic centimeters of drink? (Hint: Use a table to approximate the dimensions. There are two variables to consider the height and the radius of the circular base.) 113. Suppose a typical classroom is 7 meters wide by 10 meters long. US currency bills are 2.61 inches wide, 6.14 inches long, and .0043 inches thick. Further assume the ceiling is 3 meters high. (This is about the size of a classroom that holds 30-40 people.) If you were to fill the entire room using $100 bills, how much money could the room hold?