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Math Help - Calculating percentage capacity used...help!!!

  1. #1
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    Calculating percentage capacity used...help!!!

    The problem is:

    A water storage tank has the shape of a cylinder with diameter 22 ft. It is mounted so that the circular cross-sections are vertical. If the depth of the water is 12 ft, what percentage of the total capacity is being used?



    I'm having a bit of trouble figuring this out...please help!
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by DarthPipsqueak View Post
    The problem is:

    A water storage tank has the shape of a cylinder with diameter 22 ft. It is mounted so that the circular cross-sections are vertical. If the depth of the water is 12 ft, what percentage of the total capacity is being used?



    I'm having a bit of trouble figuring this out...please help!
    The area of the circular cross section is A=\pi(11)^2

    If we impose coordinate axes at the center of the of the circle, then the area over which the water covers is

    2\int_{-11}^1\sqrt{(11)^2-y^2}dy

    So, %= \frac{200\int_{-11}^1\sqrt{(11)^2-y^2}dy}{\pi(11)^2}
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  3. #3
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    You can calculate angle A on the attachment from

    SinA=\frac{1}{11},\ A=Sin^{-1}\frac{1}{11}

    Then calculate the volume within the sector of angle 180^o+2A

    Then calculate the area of the triangle with angle 90^o-A

    using area=0.5(1)(11)Sin(90-A).

    Double this, add the result to the sector area and divide by \pi(11)^2

    to find the ratio, then multiply by 100 for the percentage.

    You could also calculate the area of the upper sector.
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