Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. (a) Draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. Find the volumes of several such boxes. Does it appear that there is a maximum volume? If so, estimate it. (b) Draw a diagram illustrating the general situation. Introduce notation and label the diagram with your symbols. (c) Write an expression for the volume. (d) Use the given information to write an equation that relates the variables. (e) Use part (d) to write the volume as a function of one variable. (f) Finish solving the problem and compare the answer with your estimate in part (a).

Chapter 5 - Cells: The Working Units of Life 5.1. What Features Make Cells the Fundamental Units of Life Cells are the building blocks of life. st The cell theory is the 1 unifying theory of biology: - Cells are the fundamental units of life. - All living organisms are made of cells. - All cells come from preexisting cells. - Evolution through natural selection explains the diversity of modern cells. Most cells are very small (w/ the exception of bird eggs and individual cells of certain types of algae and bacteria). The reason cells are so small is because they need a high surface area-to-volume-ratio to carry out the many ≠ functions required for their survival. Its volume determines the amount of chemic