Items tagged with volume



I am taking an intermediate mathematics course. Now we are heading towards the finals and I have started to review all the topics we have been visiting during this semester.

Now I came across an excercise I cannot solve, taking into consideration what our lectures looks like and topics on the list my best bet is using lagrange multiplie method to optimize a multivariable function with constraints.

The task gives a shape that is drawn within the circle given by the equation: x^2+y^2=2.

The shape is a hexagon with 2 vertecies on the y-axsis +- the radius 2, the other 4 vertecies are the following [+-x,+-y].

I´m told that this hexagon is spinned around the y-axis to form a solid sylinder with 2 cones. The problem is to choose both radius and hight of the cylinder in order to maximize the volume.

The first problem that I dont know how i can plot this in maple, I would like to plot both the 2d hexagon and the solid spinned around the y-axsis

Also I´m not to confident what the constraint should look like.

I know how to use the lagrange multiplier by hand and can apply that inside maple, however I would like to use this opportunity to get to know the power of maple functionality more in detail.

The link provoided is an image of the hexagon, i didnt find out how to use image tags.

I saw a presentation Calculus 1 -- I'm pretty sure it was Maple -- that showed how to set up a volume of solid of revolutionvisually rotated the region and looked at it from different points of view.

Is there someplace I could go to find out ho0w to do that.  I am new and in experienced in using Maple.

Thanks in advance.

Tim Wisecarver

Georgetown preparatory School

   Hi there,

   How can we pl0t the volume or surface of revolution of cardioid r=1-cos(\theta) about  polar axis or the vertical axis in maple14.

 Any help will be appreciated.


How can I plot the volume of revolution of the region between the curves y=ln(x) and y=-ln(x)on the interval [1,e]

around the y-axis.please specify the command. I used the command: VolumeOfRevolution(ln(x),-ln(x), x=1..e, scaling=constrained,axis=vertical,output=plot). But this command only plots the revolution of the curves not the region between them.

Best Regards


of the cut-off sphere



Of course, with Maple.

How can I plot a volume (many surfaces) in X,Y, Z axis where X,Y,Z are functions in 4 variables (a,b,c,d), and the domain for the 4 variables are 

-90<=a>=90, -10<=b>=10, -12<=c>=12, -90<=d>=0,


X := proc (a, b, c, d) options operator, arrow; 324.*cos(b)*sin(c)*cos(d)+324.*sin(b)*sin(d)+323.5*cos(b)*sin(c) end procX := proc (a, b, c, d) options operator, arrow; 324.*cos(b)*sin(c)*cos(d)+324.*sin(b)*sin(d)+323.5*cos(b)*sin(c) end proc

Y := proc (a, b, c, d) options operator, arrow; (324*1.*sin(a)*sin(b)*sin(c)+324*1.*cos(a)*cos(c))*cos(d)+(-1)*324.*sin(a)*cos(b)*sin(d)+323.5*sin(a)*sin(b)*sin(c)+323.5*cos(a)*cos(c)-100 end proc

Y := proc (a, b, c, d) options operator, arrow; (324*1.*sin(a)*sin(b)*sin(c)+324*1.*cos(a)*cos(c))*cos(d)+(-1)*324.*sin(a)*cos(b)*sin(d)+323.5*sin(a)*sin(b)*sin(c)+323.5*cos(a)*cos(c)-100 end proc

Z := proc (a, b, c, d) options operator, arrow; (324*cos(a)*sin(b)*sin(c)-324*sin(a)*cos(c))*cos(d)-324*cos(a)*cos(b)*sin(d)+323.5*cos(a)*sin(b)*sin(c)+(-1)*323.5*sin(a)*cos(c)+150 end proc

Z := proc (a, b, c, d) options operator, arrow; (324*cos(a)*sin(b)*sin(c)-324*sin(a)*cos(c))*cos(d)-324*cos(a)*cos(b)*sin(d)+323.5*cos(a)*sin(b)*sin(c)+(-1)*323.5*sin(a)*cos(c)+150 end proc

I want to find  the volume contribution x^2+y^2=z and x^2+y^2=2x over xy with Maple.

I was thinking about the area problem, yet again, and found myself asking the question: why must we go through such elaborate means to get Maple to generate a plot of the region between two (or more curves)? I use the word elaborate to describe any process that would might become overwhelming, for, say a student, to go through to accomplish a task. Anyone with the most basic of backgrounds can understand the area problem, but yet, such an individual might not find it a trivial...

How to find the volume of the intersection of the sphere {(x, y, z): x^2+y^2+z^2 <= R^2 } and
the set {(x, y, z): |x| <= a, |y| <= a } under the assumptions R > a*sqrt(2) and a > 0?

I have the following problem. Two formulas in three variables represent the costs of algorithms. I want a visual of their ratio, so that I can "see" how their relative performance varies. Here is a simple example. I can analyze this example analytically, but you can't always do that.

R := sum(binomial(n+i*d,n),i=1..k-1);
S := binomial(n+k*d,n);
f := unapply(R/S, n, d, k);
A := Array(1..10,1..10,1..10,f,datatype=float[8]);

I want a 3-dimensional rendering...

Ive tried several commands, but none of them will give me a response

Here are the points im working with:

u = (2, -3, 1), v = (-4, 3, 3), w = (2, 4, 6)

And here are the several commands ive tried to use, with "with(LinearAlgebra), with(geom3d)" implemented before:


volume([2, -3, 1], [-4, 3, 3], [2, 4, 6], parallelepiped)

> with(plots, display);
> volume;
display(parallelepiped, axes = normal, scaling = constrained, orientation = ...

I currently need to cut a sphere into equal parts becuase I am carrying out an investigation for a school assignment. However, I do not know how I can cut the sphere into pieces in Maple, which I have been told it needs to be done through code. I will need to know how I can cut it so I can carry out my investigation by cutting it into different number of pieces. For example, cutting a sphere into half, so one piece would be a hemisphere.


Also, I will...

Use a change of variables to find the volume of the solid region lying below the surface f(x,y)=(2y-x)^4sqrt(x+y) and above the parallelogram in the xy=plane with vertices (3,5) (2,6) (10,10) and (11,9)

Graph the 'ice cream cone' formed ny the upper half of the sphere x^2+y^2+z^2=16 and the cone z=sqrt(x^2+y^2) using maple, and find the z-coordinates of its center of mass.

Graph the region insde the one-sheeted hyperboloid x^2+y^2-z^2=9 between z=4 and z= -4 using maple and find the volume of this region

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