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  2. Cone - Wikipedia

    en.wikipedia.org/wiki/Cone

    The volume ratio is maintained when the height is scaled to h' = r ... Any plane section of an elliptic cone is a conic section. Obviously, any right circular cone ...

  3. 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 ...

  4. Spherical cap - Wikipedia

    en.wikipedia.org/wiki/Spherical_cap

    An example of a spherical cap in blue (and another in red) In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane.It is also a spherical segment of one base, i.e., bounded by a single plane.

  5. Conic section - Wikipedia

    en.wikipedia.org/wiki/Conic_section

    A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola , the parabola , and the ellipse ; the circle is a special case of the ellipse, though it was sometimes called as a fourth type.

  6. Volume - Wikipedia

    en.wikipedia.org/wiki/Volume

    Volume is a measure of regions in three-dimensional space. [1] ... A cone and a cylinder have radius r and height h. 2. ... Section 14.4 . In cylindrical ...

  7. File:Visual proof cone volume.svg - Wikipedia

    en.wikipedia.org/wiki/File:Visual_proof_cone...

    visual proof cone volume: Image title: Proof without words that the volume of a cone is a third of a cylinder of equal diameter and height by CMG Lee. 1. A cone and a cylinder have radius r and height h. 2. Their volume ratio is maintained when the height is scaled to h' = r √Π. 3. The cone is decomposed into thin slices. 4.

  8. 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":

  9. Hypercone - Wikipedia

    en.wikipedia.org/wiki/Hypercone

    If it is restricted between the hyperplanes w = 0 and w = r for some nonzero r, then it may be closed by a 3-ball of radius r, centered at (0,0,0,r), so that it bounds a finite 4-dimensional volume. This volume is given by the formula ⁠ 1 / 3 ⁠ π r 4, and is the 4-dimensional equivalent of the solid cone. The ball may be thought of as the ...