What is the equation for an oblique cylinder centered on the origin?
Jul 28, 2020 · The equation of the cylinder will be $(x-z.tan\alpha)^2 + y^2 \le R^2$. If we want the oblique cylinder to have the same volume, $-\frac{h}{2}\le z \le \frac{h}{2}$ remains the same. EDIT: added pictures of initial position and oblique cylinder slanted towards x-axis.
Equation of an Oblique Cylinder in 3d Plane and checking if a …
Mar 6, 2022 · g(b) - b < 0,0,>0 will determine whether point b lies within the cylinder on the periphery of the cylinder or out of the cylinder.b is a 3d point(x,y,z) Now after finding numerous posts on the web I am not able to get one simple equation …
geometry - Lateral area of oblique cylinder and cone
Sep 14, 2015 · An oblique cylinder is easier since it has an entirely congruent slant height, which is congruent to the axis. So an accurate lateral area formula would be 2πra, where r is the radius and a is the axis. And what I mean by "axis" is the distance between the center of the base and the vertex. However, an oblique cone only has one pair of ...
Finding the volume of an oblique cylinder using triple integrals
Aug 7, 2020 · I want to find the volume of an oblique cylinder using triple integrals. The triple integral part is important because I plan to use the limits of integration for computing the moment of inertia te...
Volume of oblique cylinder - Mathematics Stack Exchange
Mar 9, 2014 · Oblique cylinders have the same height as regular cylinders in terms of r r and h h! To convince yourself, try this, and you'll see that an oblique cylinder is just a warped right cylinder. So if the slant angle is 60 60 degrees, the height is 3 3–√ 3 3 by the 30 − 60 − 90 30 − 60 − 90 triangle properties. So then the volume is ...
geometry - If I have an oblique cylinder can I trim it in to a ...
If I have an oblique cylinder can I trim it down into a right cylinder? I suspect the answer is no. A cut at any angle other than the one that produces a circle will produce a non-circular ellipse. What confuses me is the image of two cylinders of infinite height. One is formed by extending the oblique cylinder.
integration - Volume between an Oblique Cylinder and a vertical …
Aug 25, 2024 · Volume between elliptical vertical cylinder and generatrix can be found in following way: as $-2 \leqslant x \leqslant 2$ for elliptical base and for generatrix $(3z+y)^2+x^2=36\quad (1)$ we have $-6 \leqslant x \leqslant 6$, then elliptical vertical cylinder lies "inside" generatrix and we can find roof and floor from $(1)$.
Volume of a solid region enclosed by elliptic cylinder using triple ...
Jan 16, 2021 · Find the volume of a solid limited laterally by an elliptical cylinder $$\frac{(x-2)^2}{4}+\frac{(y-1)^2 ...
When is the intersection of a cone and a cylinder is planar?
Sep 17, 2021 · The desired cylinder's radius is necessarily the ellipse's minor radius. So, generally, there's are two families of configurations (essentially parameterized by $\theta$ and a scale factor, and the choice of cylinder axis) of cones and cylinders having (partially) planar intersection, with no requirement that the cone and cylinder have parallel ...
Cartesian equation cylinder along a line - Mathematics Stack …
Apr 8, 2016 · So now I know the equation of the cylinder, and I calculate the cross section with this cylinder Pin and the sphere. (equation in answer + sqrt(x^2+y^2+z^2)=1). Then I also know the blue plane in figure (a), which stands perpendicular on the velocity, given by ux+vy+wz=0 (plane goes through the origin of the sphere). This is the third equation.