Some years ago I taught a calculus course for especially talented students. I made up the following problem as an interesting challenge.

Take a circular disk made of paper. Cut out a sector of some angle α from the disk. Roll each of the resulting two pieces into cones. Let V(α) be the sum of the volumes of the two cones. Find the α that maximizes V(α).

Here is an animated statement of the problem, produced in Maple.

 

Hello

I am currently working on a visual proof that cutting a cone with a plane, can give you a mathematically correct ellipse.
Therefore i want to animate a cone, using the "cone" command, where you can set the origin, radius and height. I was wondering if it is possible to, using the animate command, make an animation with a cone, either chaning radius of base or height. I have tried various combinations of different commands, but have not had any success. I hope you can help me out!

- Oscar

Hi, I have the following problem:

I want to plot the cone given by 1/16*(3x^2+10xz+3z^2-16y^2) and x>=0, z>=0. I tried it with

implicitplot3d([1/16*(3*x^2+10*x*z-16*y^2+3*z^2), x >= 0, z >= 0], x = -5 .. 15, y = -15 .. 15, z = -5 .. 15, grid = [30, 30, 30], style = surface);

But the result is one surface for each inequaility and not the cone.

If i restrict the range of x and z to be 0..15 and dismiss the additonal inequalities, a big part of the cone surface is missing somehow:

Does anybody know how to fix this? Do I have to use another plotcommand?

Thanks for your help!

cone_rail_track_Maple.mws

The attached program is of a point moving along a conical path of a cone, then doing a descent back to the start.   For values R=60, r=20, h=10 the animation seems to work reasonably well.  However when r=19 - only a small change - the development plot of the cone is only partially shown?   Also, I have some variables nameP1, nameP2 which I would like to alter the color of.  Howdo I do this?

  Any comments or help most appreciated. 

 

Hi Dears,

Let us consider the following polyhedral cone which is defined by 8 inequalities (also, x,y,z ≥0): 

1. y-z ≥0

2. 3y-2z ≥0

3. 2y-2z ≥0

4. x-2y+z ≥0

5. x-y ≥0

6. 2x-y ≥0

7. x-z ≥0

8. x+y-z ≥0. 

How can we deduce that the inequalities 3 and 4 may be define this polyhedral cone and the others are redundant?

How can remove the redundant inequalities for defining this polyhedral cone?

Is there any Maple command or function that recive these 8 inequalities and return inequalities 3 and 4? In fact, inequalities 3 and 4 are facets of this polyhedral cone. 

 

Thank you in advanced. 

Sincerely yours

Hi, I am a Maple newbie. My problem is I do not know how to generate the result to find the answers of these question: 

1. a)   Sketch the surface area of the part of paraboloid z = x² + y² that lies under the plane z=8.

b)   Compute the surface area.

2. a)   Sketch the solid that lies above the cone z = (x² + y²)^1/2 and inside the sphere x² + y² + z² = 16.

b)   Compute the volume of the solid.

It is possible to calculate these question? Does anyone has a suggestion? Thank you. 

How to do for to built animation Cylinder inscribed in cone?( in optimization problem)

I am trying to graph an olique cone with a circular base, and I am having trouble learning how to generate an equation for it. Any help is greatly appreciated!

Hi,

I would like to plot a cone where I can change the vertex angle directly. I would also to be able to change the size of the cone. I have tried:

cone([r*cos(phi)*sin(theta), r*sin(phi)*sin(theta), r*cos(theta)], phi = 0 .. 2*Pi, r = 0 .. 1, theta = (1/6)*Pi, coords = spherical)

but this gives me the following error:

Error, (in plot3d) unexpected options: [[r*cos(phi)*sin(theta), r*sin(phi)*sin(theta), r*cos(theta)], phi = 0 .. 2*Pi, r = 0 .. 1, theta = (1/6)*Pi]

Thanks!

I'm trying to calculate flux through a cone but gets the following:

Flux(VectorField(`<,>`(x, y, z), cartesian[x, y, z]), Surface(`<,>`(x,y,z), x^2+y^2<=2*a,z = 2*a-sqrt(x^2+y^2)))
Error, (in VectorCalculus:-Flux) error with surface input

what I dont understand is the purpose of the second order cone constraint.

The definition is: The first element must be at least as large as the Euclidean
norm of the remaining elements. The euclidean norm for R^3 is the distance from
origo to the point [x,y,z] due to pythagores theorm ie A^2+B^2=C^2 where
C is the distance from origio to the point[x,y,z]

Again for R^3 then we have [x,y,z] then x > the euclidean norm for (y,z) which
means that x> sqrt(y^2+z^2...

Hi, i would like to put a question. suppose we have a cone, and we want to find whether a line will intersect the cone or not, how will we find this? A more challenging question would be: if the line is changing due to the movement of originating point, how would we find its intersection?