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Grass for goats (the silo version). (English)
Math. Teach. (Reston) 107, No. 7, 553-557 (2014).
From the text: The Grazing Goat problem, familiar to many teachers and students, has several variations. The version presented here provides a rich opportunity for engaging students in a project spanning several weeks. Three solutions are discussed, one suitable for a calculus class, one suitable for a geometry class, and one suitable for a pre-calculus class. Although we start with a calculus approach, most of the article uses only algebra and geometry concepts. Also discussed are the didactics of using projects to open ever-larger fields of mathematics to students. The problem maybe stated as follows: A retired mathematics professor has decided to raise a goat. He owns a silo and a barn. The barn’s front wall is tangent to the silo at the corner. The silo has a circular base with a radius of 10 feet. The professor has decided to tether the goat to a chain that is anchored at the corner of the barn, the point of tangency. He has also cut the chain so that it is long enough to wrap around the silo exactly once-that is, the length of the chain equals the circumference of the silo. Help the professor calculate the grazing area of the goat. Present a solution, complete with diagrams and calculations, explaining your answer. You are encouraged to use calculators and computers.
Classification: G43 G63 N53 I54 G44 N54
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