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Math Help - Volume and Sphere

  1. #1
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    Volume and Sphere

    A spherical ball of radius 2" is placed in a bowl in the shape of a half-sphere of radius 4". If
    the bowl is lled with water to a depth of 3", calculate the volume of water needed.

    Hint: Think of the bowl as being described by rotating part of
    the circle x^2 + (y-4)^2 = 16 around the y-axis, and the ball as
    being obtained by revolving the circle x2 + (y - 2)^2 = 4 around
    the y-axis.
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  2. #2
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    Quote Originally Posted by Jgirl689 View Post
    A spherical ball of radius 2" is placed in a bowl in the shape of a half-sphere of radius 4". If
    the bowl is lled with water to a depth of 3", calculate the volume of water needed.

    Hint: Think of the bowl as being described by rotating part of
    the circle x^2 + (y-4)^2 = 16 around the y-axis, and the ball as
    being obtained by revolving the circle x2 + (y - 2)^2 = 4 around
    the y-axis.
    Is the spherical ball attached to the bottom??? or is it floating? If it is the second case we would need to know the density of the material within the ball, thus I'll suppose it is the first case.

    In this case we may use the hint provided, all we need to do is find the volume of rotation between the curves:

     <br />
\int_{0}^{3} \pi (\sqrt{16 - (y-4)^{2} })^{2} dy - \int_{0}^{3} \pi (\sqrt{4 - (y-2)^{2} })^{2} dy <br />

    = 18 * Pi
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