MATH OLYMPIAD (1998) Session I Problem
You are visiting your uncle who owns a nursery. He has 100 boards to build the walls of a greenhouse. He will make the roof and door out of glass himself. The boards are all 2 inches by 6 inches across (2 by 6's) and are all 8 feet long. He wants you to design his greenhouse!
Here are the parts to a wall:
To make sure your greenhouse is safe, there are building code rules you must follow. They are:
Window or door width |
Header thickness |
2 feet or less |
2 inches (1 board) |
3 feet or less (greater than 2) |
4 inches (2 boards) |
4 feet or less (greater than 3) |
8 inches (4 boards) |
5 feet or less (greater than 4) |
10 inches (5 boards) |
INSTRUCTIONS
Design the walls of your uncle's greenhouse. Use the GREENHOUSE PLAN SHEET to draw neat pictures of your greenhouse. The pictures you draw should show the floor and walls of your design. Be sure to include all dimensions on your drawings. Your dimensions may be in feet and inches.
Try to meet all your uncle's requirements, stay within the building code rules, and use 100 boards or less.
Your design will be graded on how well you meet all building code rules and how well you meet your uncle's requirements. How well you meet your uncle's requirements will be measured by this quality equation:
Q = ( F + 2W )
S
This equation means that the quality of your design goes up when your studs are closer together. At the bottom of the back of the GREENHOUSE PLAN SHEET is a space for you to compute your quality "Q" and tell us why your design is best.
You have 1 hour to complete this task. Good luck!
GRADE 5: GREENHOUSE PLAN SHEET
School__________________ Team number: _____________
For your design, what is:
F (the inside floor area) = ____________ |
W (the total window area)= ____________ |
S (the stud spacing) = ____________ |
Q (the design quality) = ____________ |
SHOW US YOUR DESIGN AND TELL US WHY IT IS BEST (You may use the back)