Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

Consider the region bounded by x=4-y^2, x-axis and y-axis...?

The volume of the solid generated by revolving the region about the x-axis is given by ____ ?

2 Answers

Relevance
  • Pope
    Lv 7
    2 months ago

    There are two distinct closed regions having those boundaries, one below the x-axis and one above. They generate the same solid of revolution. It is a paraboloid. Its base radius is 2, and its height is 4.

    volume = (1/2)π(2)²(4) = 8π

  • 2 months ago

    The curve (x = 4 - y²) meets x-axis (y = 0) at (4, 0)

    The curve: x = 4 - y²   ⇒  y² = 4 - x

    Volume of the solid

        ₄

    = ∫ πy²dx

       ⁰

        ₄

    = ∫ π(4 - x)dx

       ⁰

                            ₄

    = π [4x - (x²/2)]

                            ⁰

    = π [4*4 - (4²/2)]

    = 8π

    Attachment image
Still have questions? Get your answers by asking now.