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  2. List of centroids - Wikipedia

    en.wikipedia.org/wiki/List_of_centroids

    b = the base side of the prism's triangular base, h = the height of the prism's triangular base L = the length of the prism see above for general triangular base Isosceles triangular prism: b = the base side of the prism's triangular base, h = the height of the prism's triangular base

  3. List of formulas in elementary geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities; List of volume formulas – Quantity of three-dimensional space

  4. Method of exhaustion - Wikipedia

    en.wikipedia.org/wiki/Method_of_exhaustion

    Proposition 11: The volume of a cone (or cylinder) of the same height is proportional to the area of the base. [6] Proposition 12: The volume of a cone (or cylinder) that is similar to another is proportional to the cube of the ratio of the diameters of the bases. [7] Proposition 18: The volume of a sphere is proportional to the cube of its ...

  5. Tetrahedron - Wikipedia

    en.wikipedia.org/wiki/Tetrahedron

    The volume of a tetrahedron can be obtained in many ways. It can be given by using the formula of the pyramid's volume: =. where is the base' area and is the height from the base to the apex. This applies for each of the four choices of the base, so the distances from the apices to the opposite faces are inversely proportional to the areas of ...

  6. Frustum - Wikipedia

    en.wikipedia.org/wiki/Frustum

    The volume of a conical or pyramidal frustum is the volume of the solid before slicing its "apex" off, minus the volume of this "apex": =, where B 1 and B 2 are the base and top areas, and h 1 and h 2 are the perpendicular heights from the apex to the base and top planes. Considering that

  7. Spherical cap - Wikipedia

    en.wikipedia.org/wiki/Spherical_cap

    Utilizing the pyramid (or cone) volume formula of = ′, where is the infinitesimal area of each pyramidal base (located on the surface of the sphere) and ′ is the height of each pyramid from its base to its apex (at the center of the sphere).

  8. Cavalieri's principle - Wikipedia

    en.wikipedia.org/wiki/Cavalieri's_principle

    Within the cylinder is the cone whose apex is at the center of one base of the cylinder and whose base is the other base of the cylinder. By the Pythagorean theorem , the plane located y {\displaystyle y} units above the "equator" intersects the sphere in a circle of radius r 2 − y 2 {\textstyle {\sqrt {r^{2}-y^{2}}}} and area π ( r 2 − y ...

  9. 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 ...

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