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Math Help - volume

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    volume

    Find the volume of the solid whose base is the region between the x-axis and the inverted parabola f(x)=4-x^2 if every vertical cross sections of the solid perpendicular to the y-axis are semicircles.
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    Quote Originally Posted by mikegar813 View Post
    Find the volume of the solid whose base is the region between the x-axis and the inverted parabola f(x)=4-x^2 if every vertical cross sections of the solid perpendicular to the y-axis are semicircles.
    V = \int_c^d A(y) \, dy

    y = 4-x^2

    x = \sqrt{4-y}

    radius of each semicircular cross section is x

    A = \frac{\pi}{2} x^2 = \frac{\pi}{2}(\sqrt{4-y})^2 =

    V = \frac{\pi}{2}\int_0^4 4-y \, dy
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