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2. Cone - Wikipedia

   en.wikipedia.org/wiki/Cone

   In modern mathematics, this formula can easily be computed using calculus — it is, up to scaling, the integral = Without using calculus, the formula can be proven by comparing the cone to a pyramid and applying Cavalieri's principle – specifically, comparing the cone to a (vertically scaled) right square pyramid, which forms one third of a ...

3. List of formulas in elementary geometry - Wikipedia

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

   Cone – , where is the base ... List of volume formulas – Quantity of three-dimensional space; References This page was last edited on 16 June 2023, at 16:58 (UTC ...

4. Tree volume measurement - Wikipedia

   en.wikipedia.org/wiki/Tree_volume_measurement

   The value 75.4 = 24 π, where 24 π substitutes for factor of 12 π in the formula for a volume of frustum of a cone encompassing a full tree using one base circumference, converting it to a volume formula that uses a basal circumference that is the average of circumferences C 1 and C 2.

5. Spherical sector - Wikipedia

   en.wikipedia.org/wiki/Spherical_sector

   If the radius of the sphere is denoted by r and the height of the cap by h, the volume of the spherical sector is =. This may also be written as V = 2 π r 3 3 ( 1 − cos ⁡ φ ) , {\displaystyle V={\frac {2\pi r^{3}}{3}}(1-\cos \varphi )\,,} where φ is half the cone angle, i.e., φ is the angle between the rim of the cap and the direction ...

6. Frustum - Wikipedia

   en.wikipedia.org/wiki/Frustum

   The Egyptians knew the correct formula for the volume of such a truncated square pyramid, but no proof of this equation is given in the Moscow papyrus. 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":

7. The Method of Mechanical Theorems - Wikipedia

   en.wikipedia.org/wiki/The_Method_of_Mechanical...

   The condition of balance ensures that the volume of the cone plus the volume of the sphere is equal to the volume of the cylinder. The volume of the cylinder is the cross section area, times the height, which is 2, or . Archimedes could also find the volume of the cone using the mechanical method, since, in modern terms, the integral involved ...

8. Cone (algebraic geometry) - Wikipedia

   en.wikipedia.org/wiki/Cone_(algebraic_geometry)

   In algebraic geometry, a cone is a generalization of a vector bundle. Specifically, given a scheme X , the relative Spec C = Spec X ⁡ R {\displaystyle C=\operatorname {Spec} _{X}R}

9. Volume - Wikipedia

   en.wikipedia.org/wiki/Volume

   Some SI units of volume to scale and approximate corresponding mass of water. To ease calculations, a unit of volume is equal to the volume occupied by a unit cube (with a side length of one). Because the volume occupies three dimensions, if the metre (m) is chosen as a unit of length, the corresponding unit of volume is the cubic metre (m 3).