Αποτελέσματα Αναζήτησης
5 ημέρες πριν · 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.
An elliptical cone is a cone a directrix of which is an ellipse; it is defined up to isometry by its two angles at the vertex. Characterization: cone of degree two not decomposed into two planes. Contrary to appearances, every elliptical cone contains circles.
24 Οκτ 2024 · About MathWorld; MathWorld Classroom; Contribute; MathWorld Book; wolfram.com; 13,206 Entries; Last Updated: Thu Oct 24 2024 ©1999–2024 Wolfram Research, Inc.
Definition. Cone based on the circle, ellipse, parabola or hyperbole respectively called circular, elliptical, hyperbolic or parabolic cone (the last two have infinite volume).
Assume the cone is vertical, its axis is the $z$-axis and its base is an ellipse on the $xy$-plane, centered at $(x,y,z)=(0,0,0)$, with semi-major axis $a$ and semi-minor axis $b$. The equation of the base is thus $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\qquad z=0.$$ Let $h$ be the height of the cone.
An elliptic cone is a cone with a base shaped like an ellipse. One could say that a cone is a special kind of elliptic cone with both semi-axes (a and b) being of equal length. The formula for calculating the volume of an elliptic cone is as follows: π (pi) ≈ 3.14159. V = volume. V = (π x a x b x h) / 3. © Measurement Mate.
