finalans - Final Exam Ben Ellison Spring 2007 Math 131 1...

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Final Exam Ben Ellison Spring 2007 Math 131 1 Instructions: Complete all problems. You must provide explanations for your work in order to receive credit. Circle your answers. Note: there is a reference sheet at the end of the exam with various formulas. Name Circle your Discussion Section: 9:30 2:30 Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Total

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Final Exam Ben Ellison Spring 2007 Math 131 2 1) (15 pts) Pizzas are typically sold in diameters. In other words, if you buy a 16-inch pizza, you are getting a pizza that has a diameter of 16 inches. Suppose pizza dough costs 25 cents per square foot, and that the combination of pizza sauce and cheese cost 60 cents per square foot. Finally, suppose that on a slice of pizza, there is an inch of crust (that is, the sauce and cheese is spread out to within in an inch of the edge of the pizza). Calculate the cost of a 12 inch, a 16 inch, and a 20 inch pizza. First 25 cents per square foot is about .17 cents per square inch, and 60 cents per square foot is about .42 cents per square inch. On a 12-inch pizza, the area of the dough is π (6) 2 = 36 π square inches, while the area of the sauch/cheese mixture is π (5) 2 = 25 π square inches (remember, if it has a one inch border on all sides, then the diameter is two inches less). Thus the amount of money it costs is \$ . 19 + \$ . 32 = \$ . 52, which is not a whole lot. The 16-inch pizza has area 64 π , and the sauce/cheese mixture has area 49 π . Thus, it costs \$ . 34 + \$ . 64 = \$ . 98. The 20-inch pizza has area 100 π , and the sauce/cheese mixture has area 81 π . Thus, it costs \$ . 53 + \$1 . 06 = \$1 . 59.
Final Exam Ben Ellison Spring 2007 Math 131 3 2a) (10 pts) According to wikipedia, Lake Monona has 13 miles of shoreline. What is the maximum surface area Lake Monona can have? The best area we can get is a circle. Then 13 miles would correspond to the circumference. Thus, the radius would be 13 2 π = 2 . 07 miles. Thus, the area would be π (2 . 07) 2 = 13 . 45 square miles. b) (10 pts) If, for some strange reason, Lake Monona were to be shaped like a rectangle, what is the maximum surface area it could have? In this case, the best area we could do is a square. Each side would be 13 4 , and the area would be ( 13 4 ) 2 = 169 16 = 10 . 56 square miles.

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Final Exam Ben Ellison Spring 2007 Math 131 4 3) (20 pts) One way of thinking about the Pythagorean theorem is that it says that given
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finalans - Final Exam Ben Ellison Spring 2007 Math 131 1...

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