Optimizing Volumes and Surface Areas Using
a Spreadsheet

*The U.S Postal Service will accept a
box for domestic shipment only if the sum of the length and girth (distance
around) does not exceed 108 in. Find the dimensions fo the largest acceptable
box with a square end.
*

To help you through the problem, there are several questions for you to answer. When you are asked to fill something in on your spreadsheet do so!!

1. The spreadsheet is set up for you. Just download the excel spreadsheet file girth.xls, and you're ready to go. Your first job is to fill the

*______________________________________________________________________
*

2. a) Write an expression that represents the Postal Service's specifications for acceptable boxes in terms of l (length) and g (girth).

108 = _________________

b) Solve the above equation for g. This equation will be used to find the dependent variable, g, in the spreadsheet. g = __________________

Before you type the formula into the spreadsheet in cell, C

c) Next, write an expression that represents the edge of the square end of the box, in terms of g (girth). Before you type the formula into the spreadsheet in cell, D6, write it down using the cell references. s = _______________ Type this into the spreadsheet and

3. a) Write an equation that represents the volume of the box in terms of
l (length) and s (side). volume = __________________ Now you will need to
write this formula using *cell references*. You only need to do it
for the first cell in the first row, because you will "fill down"
for the rest of the column. volume = ___________________

4. Now that the spreadsheet is filled in you need to determine the dimensions
of the largest possible box with a square end and record them here. ________________________

**problem: ***A tank with a rectangular base and rectangular sides is to be open
at the top. It is to be constructed so that its width is 4 meters and its
volume is 36 cubic meters. If building the tank costs $10 per square meter
for the base and $5 per square meter for the sides, what is the cost of
the least expensive tank?
*

1. a) Write an equation for the volume of the box in terms of h (height) and l (length). Given that the volume is to be 36 cubic meters, and the width is to be 4 meters, write an equation for the height of the box in terms of l (length).

h = _________________

2. a) Write an equation for the area of the base in terms of l (length), given the width is to be 4 meters. area of base = ________________Write an equation for the cost of materials for the base in terms of l (length), given the width is to be 4 meters. cost of base = __________________

b) Write an equation for the lateral area of the box in terms of l (length) and h (height), given the width of the box is to be 4 meters. lateral area = _______________ Write an equation for the cost of materials for the lateral area in terms of l (length) and h (height), given the width is to be 4 meters. cost of lateral area = ______________

c) Write an equation for the total cost of materials for the open box, in terms of l (length) and h (height), given the width is to be 4 meters. total cost = ______________

The formulas you have written above are all you will need to solve the problem, GOOD LUCK!!

Need more problems on which you can practice? Go on to the next page.