Project 14.1 Building a House
Simple floor plans drawn to scale are less expensive than architectural
plans. That is why builders prefer to start work from simple floor plans.
You are a builder and have been approached to quote on building the
following house.
1. What are the dimensions (in metres) of each
room and corridor?
2. What is the total floor area of the house?
Ignore the thickness of the walls.
4. What price will you quote? Assume that
the quote is based on $875 per square metre?
Your report should include the following:
- Statement of the problem in your own words
- All working and diagrams
- Conclusion
- References
- Acknowledgments
Project 14.2 Dehydration
In this project you are required to consider the ratio
of the surface area to the volume of a cube and then explain why a baby
may suffer more from heat than an adult.
We know that for a cube:
Part A
1.
a. Using a Microsoft® Excel worksheet, key in 1 in cell A4. Then insert the formula =A4+1 in
cell A5; and copy it down to cell A22.
b. To calculate the surface area of the cube, key in the
formula =6*A4^2 in cell B4 and press
Enter. The surface area of the cube is displayed in cell B4. So, the
surface area of the cube whose edge is 1 unit is 6 unit2.
c. To calculate the volume of the cube, key in the formula =A4^3 in cell C4 and press Enter. The total volume of the cube is
displayed in cell C4. So, the volume of the cube whose edge is 1 unit is 1
unit3.
d. To calculate the ratio of the surface area to the volume of
the cube of edge 1 unit, key in the formula =B4/C4 in cell D4 and press Enter. The ratio of the surface area to the
volume of the cube is displayed in cell D4. So, the ratio of the surface
area to the volume of the cube whose edge is 1 unit is 6.
e. Copy each formula down to row 22.
f. Save the file and print the worksheet.
3. Look at the cube edge and the ratio of surface area to volume; and
explain why babies dehydrate more quickly than adults.
Part B - Limiting Value
4.
a. Using another worksheet, key in 0.05 in
cell A4. Then insert the formula =A4+0.05 in
cell A5; and copy it down to cell A22.
b. Save the spreadsheet.
5.
a. Using another worksheet, key in 100 in cell A4. Then insert the formula =A4+100 in
A5; and copy it down to cell A22.
b. Save the spreadsheet.
Project 14.3 Hanging Wallpaper
Some home owners use wallpaper instead of paint to decorate
their house. Hanging wallpaper is cheaper if you do it yourself. If wallpaper
is expensive, using too much is a waste of money. So, it is important to be
able to calculate the exact amount needed for the job.
1. Use a ruler and the given scale to determine the dimensions of the
room from the plan.
2. The room is to have all walls covered with wallpaper. Guess
what the project will cost.
4. What area of the walls will a roll cover if the roll is
10 m long and 520 mm wide?
5. Find the minimum number of rolls needed to cover the
walls.
Extension
Prepare a leaflet that will contain a mathematical model (i.e. table) to
determine how many rolls are needed to paper a room of given dimensions:
a. including doors and windows
b. excluding doors and windows
Your report should include the following:
- Statement of the problem in your own words
- All working and diagrams
- Conclusion
- References
- Acknowledgments
Project 14.4 Estimating Body Surface Area
A person's body surface area is needed to work out the correct dose of a
medicine. It is difficult to measure directly the body surface
area. However, a formula that connects the body surface area to weight
and height can be used quite effectively.
The formula used for calculating the body surface area is
1. Use a calculator to estimate the body surface area of the
following patients:
a. Mr. Smith - height = 183 cm, weight = 67 kg.
b. Mr. Shepherd, height = 170 cm, weight = 50 kg.
c. Mr. Strong, height = 150 cm, weight = 65 kg.
2. Mr. Shepherd and Mr. Strong have approximately the same body
surface area, yet Mr. Shepherd is 20 cm taller than Mr Strong is. How
can you justify this?
3a. Investigate your body surface area by using the following diagram
as a model of yourself.
3b. What are the limitations of this model?
4. Compare the computational performance of the different methods. |
