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  2. Steinmetz solid - Wikipedia

    en.wikipedia.org/wiki/Steinmetz_solid

    The generation of a bicylinder Calculating the volume of a bicylinder. A bicylinder generated by two cylinders with radius r has the volume =, and the surface area [1] [6] =.. The upper half of a bicylinder is the square case of a domical vault, a dome-shaped solid based on any convex polygon whose cross-sections are similar copies of the polygon, and analogous formulas calculating the volume ...

  3. Steinmetz curve - Wikipedia

    en.wikipedia.org/wiki/Steinmetz_curve

    Steinmetz curves for various cases Steinmetz solid (intersection of two cylinders) involving Steinmetz curves (purple) A Steinmetz curve is the curve of intersection of two right circular cylinders of radii a {\displaystyle a} and b , {\displaystyle b,} whose axes intersect perpendicularly.

  4. Line-cylinder intersection - Wikipedia

    en.wikipedia.org/wiki/Line-cylinder_intersection

    The term “cylinder” can refer to a three-dimensional solid or, as in this article, only the curved external surface of the solid. This is why a line piercing a cylinder's volume is considered to have two points of intersection: the surface point where it enters and the one where it leaves.

  5. Intersection curve - Wikipedia

    en.wikipedia.org/wiki/Intersection_curve

    The intersection of two planes. The analytic determination of the intersection curve of two surfaces is easy only in simple cases; for example: a) the intersection of two planes, b) plane section of a quadric (sphere, cylinder, cone, etc.), c) intersection of two quadrics in special cases. For the general case, literature provides algorithms ...

  6. Napkin ring problem - Wikipedia

    en.wikipedia.org/wiki/Napkin_ring_problem

    Lines, L. (1965), Solid geometry: With Chapters on Space-lattices, Sphere-packs and Crystals, Dover. Reprint of 1935 edition. A problem on page 101 describes the shape formed by a sphere with a cylinder removed as a "napkin ring" and asks for a proof that the volume is the same as that of a sphere with diameter equal to the length of the hole.

  7. Shell integration - Wikipedia

    en.wikipedia.org/wiki/Shell_integration

    Shell integration (the shell method in integral calculus) is a method for calculating the volume of a solid of revolution, when integrating along an axis perpendicular to the axis of revolution. This is in contrast to disc integration which integrates along the axis parallel to the axis of revolution.

  8. 2-Year-Old Died After Dad Allegedly Isolated Him in Room Near ...

    www.aol.com/2-old-died-dad-allegedly-193803745.html

    On Dec. 2, 2023, deputies responded to a distress call at a home in West End, N.C., where they found the toddler dead. Investigators believe the child was exposed to “elevated temperatures ...

  9. Cavalieri's principle - Wikipedia

    en.wikipedia.org/wiki/Cavalieri's_principle

    In the 3rd century BC, Archimedes, using a method resembling Cavalieri's principle, [5] was able to find the volume of a sphere given the volumes of a cone and cylinder in his work The Method of Mechanical Theorems. In the 5th century AD, Zu Chongzhi and his son Zu Gengzhi established a similar method to find a sphere's volume. [2]