M408C - Notes - Worked Word Problem

M408C - Notes - Worked Word Problem - Worked Word Problem...

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Worked Word Problem Page 1 Example Kathy went to San Antone over the weekend, stopping at Marble Slab on the Riverwalk. She got a cone, one of them big ones four inches across and six inches deep. Here comes the yucky part: she eats the ice cream from a little hole at the bottom tip of the cone. When there’s two inches deep of ice cream left, she’s eating one cubic inch per minute. How fast is the height of ice cream changing, at that instant? When I say Kath’s eating ’one cubic inch per minute’ I’m talking about a rate of change: the ’per minute’ gives that away. And it’s ’cubic inches’: that’s a volume. So the basic information in the problem is that the volume of the cone is changing; the volume is a variable so it gets a name: if V denotes volume, then dV dt = - 1 in 3 min The question asks, how fast the height of the ice cream in the cone is changing. Another variable, height, denoted by h , and we’re trying to solve for dV dh .
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