Manuscript 2

# Manuscript 2 - Danielle M Henak Calculus II David Sharpe...

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Danielle M. Henak Calculus II David Sharpe October 26, 2007 Maunscript #2 The goal is to make a hydrometer. Because the hydrometer is produced by rotating the ellipse + = x216 y2 1 around the x-axis, it could also be made by rotating half of that ellipse around the x-axis. Therefore, I rotated the half ellipse = - y 1 x216 around the x-axis. To find the volume of this hydrometer, I used the volume equation: = ( ) V π f x 2 dx . Therefore, because the half ellipse intersects the x-axis when x=4 and x=-4, = - V π 44fx2 dx = - ( - ) V π 44 1 x216 2 dx = - - V π 441 x216 dx = ( - - V π x x348 44 = ( - + - ) V π 4 4348 4 4348 = ( - ) V π 8 83 Now that the volume of the hydrometer is known, we have to figure out if the hydrometer will float. We know that it will float if it has a smaller density than the water, because the less dense objects will be on top or float. To determine the density of the hydrometer, we use the equation = m pVh where m is the mass of the hydrometer, p is the density of the hydrometer, and V

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Manuscript 2 - Danielle M Henak Calculus II David Sharpe...

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