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  2. Cavalieri's principle - Wikipedia

    en.wikipedia.org/wiki/Cavalieri's_principle

    The volume ratio is maintained when the height is scaled to h' = r √ π. 3. Decompose it into thin slices. 4. Using Cavalieri's principle, reshape each slice into a square of the same area. 5. The pyramid is replicated twice. 6. Combining them into a cube shows that the volume ratio is 1:3.

  3. Paraboloid - Wikipedia

    en.wikipedia.org/wiki/Paraboloid

    This is sometimes called the "linear diameter", and equals the diameter of a flat, circular sheet of material, usually metal, which is the right size to be cut and bent to make the dish. Two intermediate results are useful in the calculation: P = 2 F (or the equivalent: P = ⁠ R 2 / 2 D ⁠ ) and Q = √ P 2 + R 2 , where F , D , and R are ...

  4. Paraboloidal coordinates - Wikipedia

    en.wikipedia.org/wiki/Paraboloidal_coordinates

    Paraboloidal coordinates are three-dimensional orthogonal coordinates (,,) that generalize two-dimensional parabolic coordinates.They possess elliptic paraboloids as one-coordinate surfaces.

  5. Parabolic coordinates - Wikipedia

    en.wikipedia.org/wiki/Parabolic_coordinates

    The red paraboloid corresponds to τ=2, the blue paraboloid corresponds to σ=1, and the yellow half-plane corresponds to φ=-60°. The three surfaces intersect at the point P (shown as a black sphere) with Cartesian coordinates roughly (1.0, -1.732, 1.5).

  6. Napkin ring problem - Wikipedia

    en.wikipedia.org/wiki/Napkin_ring_problem

    The two effects exactly cancel each other out. In the extreme case of the smallest possible sphere, the cylinder vanishes (its radius becomes zero) and the height equals the diameter of the sphere. In this case the volume of the band is the volume of the whole sphere, which matches the formula given above.

  7. Parabolic reflector - Wikipedia

    en.wikipedia.org/wiki/Parabolic_reflector

    A circular paraboloid is theoretically unlimited in size. Any practical reflector uses just a segment of it. Often, the segment includes the vertex of the paraboloid, where its curvature is greatest, and where the axis of symmetry intersects the paraboloid. However, if the reflector is used to focus incoming energy onto a receiver, the shadow ...

  8. McDonald's cup sizes around the world - AOL

    www.aol.com/lifestyle/2014-10-27-mcdonalds-cup...

    BuzzFeed collected McDonald's cups from different countries to see just how they compared -- and (un)surprisingly, cups in the USA were the biggest by far. In America, a small drink is 16 oz., a ...

  9. Interior Schwarzschild metric - Wikipedia

    en.wikipedia.org/wiki/Interior_Schwarzschild_metric

    The fluid has a constant density by definition. It is given by = =, where = / is the Einstein gravitational constant. [3] [5] It may be counterintuitive that the density is the mass divided by the volume of a sphere with radius , which seems to disregard that this is less than the proper radius, and that space inside the body is curved so that the volume formula for a "flat" sphere shouldn't ...