Thread: Math homework - find parabola

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  1. #1 Math homework - find parabola 
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    Long version:
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    Hi,
    I'm on the last question of my homework assignment which is due in a few hours and i'd appreciate it if someone could help me out as i'm not sure how to solve it:
    (The question contain two parts - i already solved the first one)

    https://i.ibb.co/ckWGj5C/illustration.png
    (this is supposed to be a cross-section of a tower)

    The first part was to find the volume of the blue section of the tower by rotating around the x-axis.

    I solved this by first finding the parabola between BC (rotated 90 degrees) and then finding the volume by rotating it around the x-axis using the equation: V = π * ∫ f(x)^2 dx
    And the way i found the parabola was just by setting up 3 true equations (C is on the parabola, B is on the parabola, and the slope of the parabola at B is 0) and then solving for it.

    This next part is the one i'm having trouble with:
    Find the volume of the blue part by rotating around the y-axis.

    I already know how to rotate around the y-axis - my problem is finding the parabola (when it isn't rotated 90 degrees) since i cant use the third equation because the slope of B would be infinity.

    I'm not given any additional information other than whats on the illustration (so i cant assume that C is the highest point of the parabola or anything like that)
    If someone knows how to solve this i'd really appreciate it - Thank you.



    Short version:
    Spoiler for Short version:
    https://i.ibb.co/ckWGj5C/illustration.png
    How do i find the parabola between B and C ?
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  2. #2  
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    Brett the Don's Avatar
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    Hope I don't have to do this math for business xD

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  3. #3  
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    are you sure that curve is meant to be parabolic with the vertex at B?

    x = (1/8)y^2 + 2 is the eq of the parabola

    integrate πx^2 dy from 0 to 8

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