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5 ημέρες πριν · A cone with elliptical cross section. The parametric equations for an elliptic cone of height h, semimajor axis a, and semiminor axis b are x = a(h-u)/hcosv (1) y = b(h-u)/hsinv (2) z = u, (3) where v in [0,2pi) and u in [0,h]. The elliptic cone is a quadratic ruled surface, and has volume V=1/3piabh.
3 Αυγ 2023 · Find the volume of an elliptic cone with a major axis of 6 units, a minor axis of 4 units, and a height of 8 units.
The elliptic cone volume calculator is used to solve the volume by giving the semi-axes and height. Easy to use. Try it now.
The cone cross section at height $z$ is an ellipse with semi-major axis $$x_1=a\left( 1-\frac{z}{h}\right) $$ and semi-minor axis $$x_2=b\left( 1-\frac{z}{h}\right) $$ by similarity of (right) triangles, as shown in the following sketch:
Elliptic cone. Other name: degree-two cone (implying: non-decomposed). Reduced equation: (with , cone of revolution if and only if a = b). Sections by the plane z = k are ellipses with half-axes ak/h and bk/h. Developable ruled quadric. Cartesian parametrization: .
This function calculates various properties of an elliptic cone. To perform the calculation, enter the two radii and the height of the elliptic cone. Then click on the 'Calculate' button.
There are four types of cones: circular, elliptical, right, and oblique. In the figure left, keep sliding the number of sides and see that as the number of triangular faces increases, the pyramid begins to look more and more like a cone. So, a cone is also a pyramid, and its fifth type is n = ∞.
