A box with square base and no top is to hold a volume {{MATH_1}}. Find the dimensions of the box that requires the least material for the five sides. {{CMD_2}} {{ENV_3}} {{CMD_4}} {{CMD_5}} The dimensions that will result in "least material" for the five sides are dimensions that result in "smallest surface area". So, the quantity that we have to "minimize" is the surface area, {{MATH_6}}. {{CMD_7}} {{CMD_8}} We have to "minimize" the surface area, {{MATH_9}}. {{MATH_10}} Remember, no top! {{CMD_11}} {{CMD_12}} Next, we express {{MATH_13}} as a function of, say, {{MATH_14}}. In order to do that, we have to express {{MATH_15}} in terms of {{MATH_16}}.