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Math Help - Water in a Tank - Integration

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    Water in a Tank - Integration

    a tank on a water tower is a sphere of a radius of 50 feet. determine the depths of the water when the tank is filled to one-fourth and three-fourths of its total capacity. use root finding capabilities of a graphing utility after evaluating the definite integral

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    Quote Originally Posted by rawkstar View Post
    a tank on a water tower is a sphere of a radius of 50 feet. determine the depths of the water when the tank is filled to one-fourth and three-fourths of its total capacity. use root finding capabilities of a graphing utility after evaluating the definite integral

    Please Help
    consider the circle x^2 + y^2 = R^2 centered at the origin.

    rotation of this circle about the y-axis yields the sphere.

    volume of the sphere ...

    V = \pi \int_{-R}^{R} R^2 - y^2  \, dy = \frac{4\pi}{3} \cdot R^3

    let h = variable water level in the tank from the bottom.

    \frac{V}{4} = \frac{\pi}{3} \cdot R^3 = \pi \int_{-R}^h R^2 - y^2 \, dy

    ... solve for h.

    once you determine h , it should just take a little thought (no calculus) to determine the level where the tank is 3/4 full.
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