Finally, simplifying, showing x as a function of y: In this case, because $x^2+y^2=z^2$ and $z^2$ can be equal to the radius, that gives $x^2+y^2=2$. Radius of each discĪttempting to follow this video, I was able to see that I could write the radius of each disc as a function of y by using the Pythagorean theorem. The Volume of a disc is $\pi r^2h$ so while the height of each disc will end up being equivalent to dy, I will have to find radius as a function of y for every disc.
To find the force I first need to find the volume of each disc and then multiply by the density, which the problem says is 62.4 lb/ft, so I only need to find the volume of each disc. To do this I am using the "disc-method" which subdivides a 3d solid into discs, in this case, a dome.
To find the Work I first needed to find the Force because Work = force*distance. How much work is required to fill the tank with water through a hole in the base when the water source is at the base? (The weight-density of water is 62.4 pounds per cubic foot.) A hemispherical tank of radius 2 feet is positioned so that its base is circular.
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