sphere of raadus2?

a sphere of radius 2 is centered at the origin. A hole of radius1 is drilled though the sphere, with the axis of the hole lying on z axis . Describe the solid region that remains in a) cylindrical coordinates and b) spherical coordinates.

that is express each coordinate variable as a double inequality of the form.

a) ?<r<?

?< theta<?

?<z<?

b) ?<p<?

?<theta<?

?<qp<?

1 Answer

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  • Anonymous
    1 decade ago
    Favorite Answer

    ♠ draw a picture; it always helps;

    sphere’s eqn: x^2 +y^2 +z^2 =R^2;

    ball: R<=2; hole: r < 1;

    subtracting these solids we get a bead:

    x^2+y^2 >= r^2 =1, x^2 +y^2 +z^2 <= R^2 =4;

    thence z^2 <= R^2 –r^2, |z| <=√(R^2 –r^2) =√3;

    ♣ polar coords: x=p*cost, y=p*sint,

    where 0 <= t < 2pi;

    bead: 0 <= t < 2pi, 1 <= R <= 2, |z| <= √3;

    ♣ spherical coord: p=R*cosq, z=R*sinq,

    where –pi/2 <= q <= pi/2;

    bead: 0 <= t < 2pi, 1 <= R <= 2, |q| <= atan(√3) or

    –pi/3 <= q <= +pi/3;

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