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March 27, 2017

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What is the volume of a spherical dome with radius 5.5ft and height 3.5ft?

  • calculus - ,

    Hmmm. Exactly what is height? Is this a truncated sphere?

  • calculus - ,

    The way I read this:
    A spherical cap is cut off giving a truncated sphere as bobpursley suspected.

    Look at

    http://en.wikipedia.org/wiki/Spherical_cap

    to see how we can find the volume of that cap.
    Volume = (πh/6)(3a^2 + h^2) , where a is the radius of the circular base of the cap, and h is its height.

    To find a, look at a cross-section, and
    a^2 + 2^2 = 5.5^2
    a^2 = 26.25

    and our h = 3.5

    volume of cap = (3.5π/6)(3(26.25) + 3.5^2)

    volume of whole sphere = (4π/3)(5.5^3)

    subtract the volume of the cap from the volume of the sphere.

    I will let you do the rest of the button-pushing.

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