1. Each member of your group needs to nd a rectangular piece of paper. 1What are the dimensions of your paper? 1What is the area of your paper? 2. Cut squares out of each of the corners of the paper and fold up the aps to create an open-top box (see the picture below}. 'What are the dimensions of your box and what is the volume of the box? Each person will turn in a picture of their box along with an expression of the Is? 3. Generalizing the ideas from part (1) and part (2), solve the following problem using a system of nonlinear equations: A rectangular piece of cardboard, whose area is 216 square centimeters, is made into an open box by cutting a 2centimeter square from each corner and turning up the sides. If the box is to have a volume of 224 cubic centimeters. what size cardboard should you start with? 4. A box, open at the top, is to be made 'om a rectangular piece of cardboard that is 30 in. long and 2D in. wide. The box can hold itself together by cutting a square out of each comer, cutting on the interior solid lines, and then folding the cardboard on the dashed lines. Express the volume of the box as a function of the indicated variable x. .1." .r 3 x l is) {h}