MTH 151 – Mathematics for the Liberal Arts I
Geometry Application Directions

Purposes
This assignment will help you practice applying what you have learned about geometry to real problems or situations, and communicating about mathematical ideas with others.

Directions
Pick a problem:
Find a problem in your home, school, or work life that you can solve using the geometry that you learned in this unit.  Many common problems, like figuring how much paint you will need to paint a room, or how many feet of wrapping paper are needed to wrap a number of gifts, use area, perimeter, or volume calculations.  The Pythagorean theorem is useful in calculating the heights and lengths of object that can’t be easily measured.  Anyone working in the field of computer graphics will encounter geometric transformation problems.
Solve the problem:
Use the geometry learned in this unit to solve your problem.  The better you use the appropriate mathematics to correctly solve the problem, the more points you will earn.
Present the problem and your solution to the others in the class:
Post a message in the application discussion forum for this unit.  In your message, describe the problem and how you solved it.  Use the equation editor as necessary to show the mathematical operations.  The better you communicate, the more points you will earn.  If you enjoy and know how to use multimedia, such as video, audio, and graphics, you may use those as well, but this is not required.
View and respond to the geometry problems submitted by your classmates.
Pick two of your classmates’ applications that were particularly helpful to you.  Write a response to each, explaining in a paragraph or two why their applications helped you better understand the mathematics for this unit or better understand how the mathematics for this unit could be used outside of class.

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Example:  
It’s been a dream of mine to have a pet piranha. Most experts recommend a single piranha be kept in an aquarium of a volume no less than 30 gallons. One day while buying t-shirts at the thrift store I noticed a fish tank on sale for one dollar, however the volume of the aquarium is not marked. 

Measuring the aquarium let me know its dimensions are 30in long, 17 in wide, and 24 in height and I know that there are 231 cubic inches of water in a gallon. Is this aquarium big enough to hold a single piranha?

First we can calculate the volume of the aquarium with the following formula:

V=lhw   so after entering the values we have   V=30*24*17 or V=12,240 in3

We can then divide our cubic inch volume by 231 to find the total gallons of the aquarium.   12,240/231= 52.9870 gallons

Its almost 53 gallons! This inexpensive aquarium would give my prospective pet more than enough room to roam.

OR

Statement of the problem
I need to find the volume of a strangely shaped container, and I don’t know any formula to calculate this volume from measuring portions of the outside of the container.

Solution of the problem
I realize that the volume of water will not change, no matter what its shape.  Therefore, I fill the strange container with water, and then pour the water into a cylindrical container of known radius r. I measure the height of the water h.
The volume of the water is then cubic units.
This is also the volume of the strange container.

Other Topics:  carpeting, room design, gift wrapping, fish tank volume, countertop replacement, shortest routes

Grading Rubric:
Grading Criteria	Points Possible	
The problem:
•	Is it a real-life problem?
•	Is it challenging, not trivial?	5	
The strategies:
•	Are one or more general problem solving strategies used?
•	Are the strategies correctly identified?	5	
The presentation:
•	Is the problem explained well?
•	Are the problem solving strategies explained well?
•	Are the appropriate terms used?	3	
Your responses:
•	Did you post at least two responses?
•	Did you explain how the examples helped you better understand the math in this unit?
•	Did you ask questions for clarification or make suggestions on how to change or improve the original application posting or any other follow-up postings?	2