Cone Definition and 514 Threads

Hi, I was reading my astrophysics textbook and came across solid angles. I'm not sure I fully understand, for example there was a problem in the book that went as follows. The attached "math.jpg" shows a light source (yellow) in the centre of an arc. The problem is 2D, but the arc is...

Homework Statement A cylinder of height 45mm and radius 12mm is placed inside a circular cone. What are the dimensions of the cone with the smallest volume to enclose this cylinder Homework Equations v=1/3(pi)r^2h v=(pi)r^2h SA=2(pi)rh The Attempt at a Solution I substuted values...

I have a set of given vectors, I want to find a rotation matrix to convert them to vectors belong to surface of a cone with vertex is origin(vectors with the same slant angle but different tilt angles). Is there anybody know what is the solution? Thanks

Hello, So I'm doing some independent study and I'm at a loss for this problem. Homework Statement Let's say we have an ellipse of the form (x2)/a + (y2)/b = 1 which we obtain by slicing a plane through a right circular cone with an opening angle of \theta (a fixed constant). We know...

Homework Statement A solid truncated cone is made of a material of resistivity 5.10 Ohm*m. The cone has a height h = 1.16 m, and radii a = 0.34 m and b = 0.84 m. Assuming that the direction of current is parallel to the axis of the cylinder, what is the total resistance for this cone? (Use...

Homework Statement A right circular cone has vertex down and is 10 feet tall with base radius 5 feet. The cone is filled with a fluid having varying density. The density varies linearly with distance to the top. Here "varies linearly" means the quantities are related by an equation of at most...

Hello :) I have been giving a mathematical problem. But I find difficulties solving this. Therefore, I will be very grateful if anybody might wanted to help? The problem is "Let K be a compact convex set in R^n and C a closed convex cone in R^n. Show that ccone (K + C) = C." - Julie.

Hi, I'm in first year physics this year and each group in my class has been tasked with making a rocket. Since we're using old pepsi bottles, we just need to make a nose cone, tail fins, and perhaps a little paper on the main body to draw a design on it. I looked a little bit online, but I...

Homework Statement let c be the curve of intersection of the cone z= sqrt(x^2+y^2) and the plane 3z= y+4, taken once anticlockwise when viewed from above. (i) evaluate ∫c (sinx - y)dx +(x+cosx)dy + (e^z + z)dz (ii) let s be the surface of the cone z= sqrt(x^2+y^2) below the plane 3z=...

Hi, so this morning I made an attempt at this... With javascript (website programming language) I was able to successfully yield the ratio of the volume of a cone compared with the volume of a cylinder (1/3). This is the source code: And basically this is the idea. It's a summation of the...

Homework Statement Show that the volume of an upright cylinder that can be inscribe in an upright cone is 4/9 times the volume of cone Homework Equations volume of cone volume of cylinder differentiation ?? similarity of triangle The Attempt at a Solution I draw the picture of...

What will be the limiting conditions?

1. A light, hollow cone is filled with sand set spinning about a vertical axis through its apex on a frictionless bearing. Sand is allowed to drain slowly through a hole in the apex. Calculate the fractional change in angular velocity when the sand level has fallen to half its original value...

So if you take a sphere with coordinates (r, \theta,\phi) and keep \theta constant you get a cone. The geodesic equations reduce to (by virtue of the euler - lagrange equations): \frac{\mathrm{d} ^{2}r}{\mathrm{d} s^{2}} - r\omega ^{2}\frac{\mathrm{d} \phi }{\mathrm{d} s} = 0 where \omega =...

Homework Statement Hi there. I haven't used iterated integrals for a while, and I'm studying some mechanics, the inertia tensor, etc. so I need to use some calculus. And I'm having some trouble with it. I was trying to find the volume of a cone, and then I've found lots of trouble with such a...

I'm given a problem where I need to parameterize a cone, but only the segment between two planes, being z=2 and z=3. This is what I ended up with: r(u,v)=(ucos(v),u(sin(v),u) u:[2,3] v:[0,2\pi] Is this right?

Homework Statement Find the Dimensions of the right circular cone of minimum volume which can be circumscribed about a sphere of radius 8 inches.Homework Equations N/A The Attempt at a Solution So this is my try, i did the question to find the minimum volume of the cone, For Larger Size...

Homework Statement Consider the two-dimensional spacetime spanned by coordinates (v,x) with the line element ds^2=-xdv^2 +2dvdx Calculate the light cone at a point (vx) The Attempt at a Solution I don't even know how the light cone for flat spacetime is calculated. So if that one's...

Hey all. I had a question. What makes the different cone cells in your eye respond to different wavelengths of light? I know that light strikes Retinal and causes it to undergo photoisomerisation, which starts the chain that leads to you seeing something. Do the different cone cells contain...

Homework Statement A cone has the base radius of 8 cm and height of 10 cm. The height of the cone is changing at at a rate of 1cm/hour whilst radius of the base is changing with it keeping the volume constant. At what rate is the surface area of the entire cone changing at this exact...

Homework Statement The height h of the cone is 1/3 of l the circumference of the base . Homework Equations Calculate the angle alpha. Give your answer with 2 decimals. The Attempt at a Solution h=1/3 * 2*Pi*r and then we don't have the radius

Homework Statement Evaluate the volume inside the sphere a^2 = x^2+y^2+z^2 and the cone z=sqrt(x^2+y^2) using triple integrals.Homework Equations a^2 = x^2+y^2+z^2 z=sqrt(x^2+y^2) The solution is (2/3)*pi*a^3(1-1/sqrt(2)) The Attempt at a Solution I first got the radius of the circle of...

hello, I need help finding the moment of inertia of a cone using triple integral. can you also explain how can we get dV with details?

Hi! If we have a 2x2 matrix [x y;y z] belonging to a positive semidefinite cone. Why is it equivalent to say x>=0, z>=0, and xz>=y^2? Thanks!

Homework Statement A water tank is shaped like an inverted cone with height 6 m and base radius 1.5 m If the tank is full, how much work is required to pump the water to the level of the top of the tank and out of the tank? Homework Equations Integral of ( density * g...

Homework Statement This is an optimization problem but I'm having trouble modeling the question. There is a sphere encased in a cone. The sphere has a fixed radius R and the cone has a variable height h and radius r. There is also a variable angle theta at the base of the cone. Express the...

Homework Statement I'm working out of Griffith's "Intro to Electrodynamics" and the problem states: "A conical surface (an empty ice-cream cone) carries a surface charge \sigma. The height of the cone is h as is the radius of the top. Find the potential difference between points a (the...

Homework Statement Let Y be a topological space. Let CY denote the cone on Y. (a) Show that any 2 continuous functions f, g : X --> CY are homotopic. (b) Find (pi)1 (CY, p). Homework Equations I have no idea. The professor said one problem would be way out in left, to see who could make the...

Homework Statement A water tank the shape of an inverted circular cone with a base radius of 2m and height of 4m. if water is being pumped into the tank at a rate of 2m^3/min, find the rate at which the water level is rising when the water is 3m deep. dv/dt = 2m^3/min h = 3m r = h/2...

Homework Statement A cone with height h and radius R. The radius R is located at the top of the cone. We have to find moment of inertia of the cone. The disc has a radius r, height of dz, and is located z below the circular surface with radius R. Homework Equations dI = \frac{1}{2}\ dm\ r^2...

Homework Statement From Goldstein's Classical Mechanics (Chapter 5 - Exercice 17 - Third Edition) A uniform right circular cone of height h, half angle A, and density B rolls on its side without slipping on a uniform horizontal plane in such a manner that it returns to its original position...

Homework Statement I have been searching online for help with this equation but have found nothing at this stage. I am looking for an equation to satisfy the Volume of a Frustum of a cone. The liquid level is measured via a sensor located in the centre point, top circle(area) of the...

I need help understanding a problem for my homework assignment. I'm not sure how to set up the problem. If anyone could help I would greatly appreciate it. Homework Statement Water is being pumped into an inverted conical tank at a constant rate. However, water is also leaking out of the...

Show the intersection of complex sphere (|z1|^2+|z2|^2+|z3|^2=1) in C^3 and the complex cone (z1^2+z2^2+z3^3=1) in C^3 is a smooth submanifold of C^3. I am trying to do it using regular level set, but I am not sure which one of (1,0) or (1,1,0) should be set to be the regular value?

Hi, I know that you can determine that the Gaussian curvature of a cone tends to infinity at the vertex, but seeing as the curvature anywhere else on the cone is zero, how is this possible?

Homework Statement Using integration, Find the Volume of a right circular cone with height h and base radius r The Attempt at a Solution since the volume is V(x) = \int A(x) d(x) so I divided the cone into horizontal circles with radius r and r = \sqrt{s^{2} + y^{2}} where is the hypotenuse...

Hello everyone, I have been stuck on this geophysics question I have for one of my classes and I really need some help with it. Can anyone solve this question. If you do, please show me how because I am really stuck here. I am stuck on both a and b. Click the link below to see the question...

Finding the volume of a cone with a elliptic base! Homework Statement The area of an ellipse is (pi)ab, where a and b are the lengths of the semimajor and semiminor axes. Compute the volume of a cone of height h = 20 whose base is an ellipse with semimajor and semiminor axes a = 4 and b = 6...

Hi, I have a cone on the z axis with his summit on height h meeting a cylinder on the x axis. The expressions should be: cylinder: y2+z2=r2 cone: x2+y2 =(z-h)2tan(phi)2 If we consider any straight line on the cone, what is the length of this line inside the cylinder? Is it...

I was looking for a paper or textbook that would provide "working equations" for Tipler Cylinders. In other words, is there an equation(s) that would provide the light cone tilt angle as a function of the cylinder's diameter, height, density, and angular velocity?

Homework Statement Consider a vertical cone of height h whose horizontal cross-section is an ellipse and whose base is the ellipse with major and minor semi-axes α and β. Verify that the volume of the cone is παβh/3. [ Hint: The area of an ellipse with major and minor semi-axes α and β is...

[PLAIN]http://img688.imageshack.us/img688/3941/fingernorm.jpg Because the cone is being held up, I said mg=2fy, where f is the friction force, so mg=2uNcos(x) (where x=theta), and I got N=mg/(2ucos(x)). The cone also isn't moving from side to side, so I said Nx=fx, so fsin(x)=...

Homework Statement I am basically given a cone with uniform volume charge and told to find the area of highest electric potential. Homework Equations I want to use the equation: V= q/4piEr The Attempt at a Solution I am having trouble finding anything in my book. I am comparing...

1. Homework Statement [/b] A small block with mass m is placed inside an inverted cone that is rotating about a vertical axis such that the time for one revolution of the cone is T. The walls of the cone make an angle v with the vertical. The coefficient of static friction is between the...

Hi, If you have a cone (right angle) with radius r, slant length l, how is the central angle theta = 2*pi*r/l? Thanks, Ivan77

What data do you need to calculate the failure point of a truncated cone when it is under uniaxial stress acting downward on the cone? The cone will be under stresses of roughly 30 tonnes and probably constructed of plastic. Thanks,

What data do you need to calculate the failure point of a truncated cone when it is under uniaxial stress acting downward on the cone? The cone will be under stresses of roughly 30 tonnes and probably constructed of plastic. Thanks,

Hi, If the cone is cut with a plane such that an ellipse has been formed. Let's say the major axis is 'a' and the minor axis is 'b'. Is there a way to find a and b from the geometry instead of getting them from the quadratic equation.

Homework Statement Water is leaking out of an inverted conical tank at a rate of 6500 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the...

Homework Statement Use polar coordinates to find the volume of the given solid: Under the cone z = Sqrt[x^2 + y^2] Above the disk x^2 + y^2 <= 4 2. The attempt at a solution I tried using formatting but I couldn't get it right so I'll explain...I changed variables by making the upper and...