Cone Definition and 514 Threads

My calculations show that until about 3.8 Gy ago (z ~ 1.7) the volume of space defined by our light cone had a high enough density to constitute a black hole, in the sense that 2GM > c2r. The further back in time, the more our light cone exceeded that threshold, because the density increases...

Hello all, I'm trying to calculate the float line on a conical shaped vessel in water. The properties of the vessel are: Weight - 10kg Area of base of vessel - 0.311m2 I am using an equation I came across here: http://answers.yahoo.com/question/index?qid=20080317200108AA5yNzY"...

you are given a contour map of a hill from which you are to approximate a cone and hence find volume. each contour is an ellipse my question: does centreing the ellipses effect the volume. I am pretty sure it doesn't but i want to verify also. if i created 4 linear lines from the...

Wow, I should really know this but I can't think of it. Let's assume (totally assume, haha) that I have a flanged cone with a flow through it. The flange is of course going to have a reaction force on it based on the flow. I know that summing forces, I have forces at the inlet and outlet (pA)_1...

Homework Statement find the anverage heigh of z=sqrt(a^2-x^2-y^2) constricted by the cone x^2+y^2<=a^2 in the xy plane Homework Equations Average Height =(1/area)*double integral of region of [z]drdpheta The Attempt at a Solution I really have no idea how to solve this problem can...

Consider a cone's surface with its vertex subtending a right angle and its base removed. If its interior were silvered, how would an observer on the axis of symmetry appear in its reflection?

Homework Statement find the point closest to the origin on the curve of intersection of the plane 2y+4z=5 and the cone z^2=4x^2+4y^2 Homework Equations The Attempt at a Solution see 40 attachement. I found the used f(x,y,z)=x^2+y^2+z^2 and found its gradient. found ggrad and...

Homework Statement A 3kg ball moves at constant speed in a horizontal circle on the inside of a cone. The radius of the circle is 2m. Determine the magnitude of the normal force acting on the ball and the time required for the ball to complete exactly one circle. Assume that the surface of the...

Homework Statement when powder or granular solids are piled up. the powder forms a conical pile. the edge of the pile reaches a certain maximum angle with the horizontal, called the angle or repose. A) a pile of coal is found to have an angle of repose of 38% what is the relationship...

I'm currently trying to read a paper and it's not making much sense. Don't feel I expect anyone to read it in detail but it might give you an idea of the lack of understanding I am having. In all honesty I don't think it's terribly well written, coupled with the fact that I'm thick and only half...

Homework Statement A tank is in the shape of an inverted right circular cone with a radius of 10 feet and a height of 6 feet. Assume the tank contains water to a depth of 4 feet. Find the work required to pump all but 1 foot of water from the tank. Homework Equations W=\int^{b}_{a}Fdx...

hi all, Ive been sitting up so late trying to work something out. If anyone could help that would be great. How do i calculate the height of a cone if the internal angle of the cone at the top vertex is 60degrees and the total volume for the cone is 2.0m3? this is just a example - if...

Find the volume of the portion of cone z^2 = x^2 + y^2 bounded by the planes z = 1 and z = 2 using spherical coordinates I am having trouble coming up with the limits Relevant equations dV = r^2*sin(theta)*dr*d(theta)*d(phi) r = sqrt(x^2+y^2+z^2) the problem is actually 2...

Homework Statement Write an evaluate a triple integral in spherical coordinates for the volume inside the cone z^2 = x^2 + y^2 between the planes z=1 and z=2. The answer is 7π/3 The Attempt at a Solution Substitute values to work out the limits. From z^2 = x^2 + y^2, substitute for...

Homework Statement "A solid cone is bounded by the surface \theta=\alpha in spherical polar coordinates and the surface z=a. Its mass density is p_0\cos(\theta). By evaluating a volume integral find the mass of the cone. Homework Equations The Attempt at a Solution I can't figure...

Find the volume of a frustum of a right circular cone with height h, lower base radius R, and top radius r. I don't want the answer. I want to know how to do this. My math teacher gave all of these problems for the class to do, but didn't explain anything. Are there equations that I can...

I want to build a porter governor to control the speed of a shaft via a varible dia double cone pulley. The speed range to be considered is b/w 250-750 rpm. I would like to know the equations involved. My textbook provides theoretical equations, I would be obliged if I could get the actual...

In the Venturi effect, in the reduction in pressure and increase velocity on the inside of the convergent cone, does the exit of the liquid on the divergent side mean the pressure that is increased (velocity decreased) can only increase to the maximum pressure that was achieved on the inside...

Just wondering about the shape of a light cone. On the attachment below, if I were standing at A and pointed a flashlight in the positive time direction, it would form the cone show, correct? Is this cone a perfect cone? For instance, if I were standing on the north pole and pointed a...

1. A right circulat cone of constant density (5kg per m^3) is 4 meters from the base to the tip. the diameter of the base is 6 m. find each of the following using inergrals A) Find the volume and mass of the cone B) find the center of mass of the cone C) find the moment of inertia of the...

An ellipse is a conic section. If you construct an ellipse using a cone, does the axis of the cone cross through one of the foci of the ellipse? if so, how can this be shown mathematically? This is just purely out of curiosity.

I have a cone filled with liqid with radius R and height H rotating with \omega. Where do we have to drill a hole that the water would spray to the maximum distance from the cone? I used the Bernoulli equation obtainig p_0+0.5 \rho {v_1}^2=p_0+0.5 \rho v^2 v is the speed at the hole...

Homework Statement A right circular cylinder is inscribed in a cone with height h and base radius r. Find the largest possible volume of such a cylinder. I'm just really confused on how to figure this one out. The equation for the volume of a cone is v = 1/3pi r^2h and the volume of a...

1. Find the electric field at the tip of a cone of height and radius R with uniform surface charge density \sigma . I get that the field diverges at the tip, which is puzzling because it's not as though there's a point charge at the tip. I thought this sort of thing can't happen when you...

Homework Statement Given Parameterization: x = u cos \phi y = sin \phi z = u cot \Omega Find the sloping surface of a right cone with semi-angle \Omega with a base radius of a. Homework Equations Surface area of a cone = \pi r\sqrt{r^2 + h^2} The Attempt at a Solution...

I am looking to test detect if a cone (described by an apex, angle theta and axis) and a sphere (defined by a sphere centre and a radius) intersect. Please see here for a complete description (because i can't post the code here)...

Perhaps someone with a lot of patience would help me. I am watching Roger Penrose Clocks at the Big Bang 09/30/2008 on PIRSA http://streamer.perimeterinstitute.ca/mediasite/viewer/NoPopupRedirector.aspx?peid=940fba57-4cf9-4659-9c2d-1324d45cf4e4&shouldResize=False# At about 37 minutes...

Homework Statement Calculate the moment of inertia of a uniform solid cone about an axis through its center. The cone has mass M and altitude h. The radius of its circular base is R. (see attached photo) Homework Equations I know I need to somehow use the equation I= intergral r^2 dm...

Homework Statement Calculate the moment of inertia of a uniform solid cone about an axis through its center. The cone has mass M and altitude h. The radius of its circular base is R. (see attached photo) Homework Equations I know I need to somehow use the equation I=\intr2dm also, I...

I posted a similar question under cosmology but the question was unable to be answered. I thought I would try a reframe the question. When approaching a black holes event horizon, the exit cone for light become smaller until it is eliminated at the event horizon itself. But how can gravity...

Homework Statement Triple integral of 1+z inside the cone z=2sqrt(x^2+y^2) above the xy plane and bounded by z=6 Homework Equations The Attempt at a Solution when z=6, 6=2sqrt(r^2) so r=3 limits of integration are z=6 to z=2r r=3 to r=-3 theta=2pi to theta=0 Just want to make...

Homework Statement So there's about 4 problems that iI just don't understand. The first one is called H20 in the S-K-Y. Theres a drawing and it kind of looks like a graduated cylinder with a circle on top. It says the spherical top holds a little over 54,000 gallons of water, the base of...

Homework Statement The question is to derive the surface area of a cone. Homework Equations slant= square root ( r^2 + h^2) surface area= int int [square root(fx^2 + fy^2 +1) da] surface area of cone side= pi *r(r^2+h^2) 3d cone formula: z= h/r(squareroot x^2+y^2) The Attempt at...

Homework Statement Hi Im having some difficulty with the following question: Figure P1.14 shows a frustrum of a cone. Of the following mensuration (geometrical) expressions, which describes (a) the total circumference of the flat circular faces, (b) the volume, and (c) the area of the...

Please I need a respectable proof how to get the volume of the truncated cone. I need it really quick. So please could you help me. No numbers just "the method" how to get that formula. Thanks.

1. The problem statement The problem requires me to calculate the flux of F=x^2 i + z j + y k out of the closed cone, x=sqrt(y^2 + z^2) with x between 0 and 1. I am having trouble approaching this problem because most of the problems I have done give the curve as z=f(x,y) instead of...

Dear All I have a problem that can be represented in two different forms. Problem is related to propagation of waves in 2D space with respect of time. I have three random points in the 3D Space. How many right circular, infinite cones with specific predetermined angle between conical...

Homework Statement You look directly overhead and see a plane exactly 1.4·km above the ground, flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.4·km. (a) Find the angle of the shock wave cone. (b) Find the...

Homework Statement A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. If water is flowing into the tank at a rate of 10 cubic feet per minute, find the rate of change of the depth of the water when the water is 8 feet deep. Homework Equations Cone: V= (Ah/3) Right...

Lets assume we have a resistor material, with a perfect solid spherical shape and no defect, we connect it from south pole to north pole, by using the general formula of R=(rho)L/A where rho is the resistivity and L is the length of the resistor, and A is the cross sectional area. I found that i...

The question is this: find the centroid of the half-cone sqrt(x^2 + y^2) <(oet) z <(oet) 1 and x >(oet) 0 (oet being or equal to, I apologize for the lack of sophistocated symbols). I thought I was doing it correctly, but my answers do not match up with those in the book. I assumed...

Homework Statement A cone rolls on a flat surface. The instantaneous axis of rotation lies parallel to the point where the cone touches the surface and the angular velocity OMEGA. The motion of the center of mass (Vcm) plus a rotation OMEGAcm about the center if mass. Describe this motion by...

If there is a frustum with base radii of 1.75 and 1.25 inches, and a height of 6 inches, what is the volume? I tried to use the V=|(b1*h1)/3-(b2*h2)/3)| from the Wikipedia page, but h2 is unknown. I get an answer of 42.41 in^3. Is this correct? Please use basic calculus as that is all I have...

1. The slant edge of a right circular cone is 6 cm in length. Find the height of the cone when the volume is a maximum. 2. Find the maximum volume of a right circular cone whose slant edge has a constant length measure a.

Suppose you wanted to make an ice cream cone that would hold as much ice cream as possible (do not assume ice cream comes in spheres). Challenge I Cut a wedge from a circle and remove it. From the remaining piece of the circle into a cone. Find the angle of the wedge that produces the cone...

Homework Statement Find the volume of an ice cream cone bounded by the sphere x^2+y^2+z^2=1 and the cone z=sqrt(x^2+y^2-1) Homework Equations The two simultaneous equations yield x^2+y^2=1 The Attempt at a Solution Attached

Hi, I'm working on a related rates problem, and I need to find the derivative of the volume of a cone. So the equation is: V = (1/3) (pi) (r^2) (h) I'm not sure how to find the derivative. Would the whole thing turn out to be 0? Or do I need to use the product rule? Please help...

Homework Statement The volume of a right circular cone is V = [(pie)(r^2)(h)]/3 and it ssurface area is S = (pie)(r)(r^2+h^2)^(1/2), where r is the base radius and h is the height of the cone. Find the dimensions of the cone with surface area 1 and maximum volume. The Attempt at a Solution...

A 0.25 kg pine cone falls from a branch 20 m above the ground. A) With what speed would it hit the ground if air resistance could be ignored? m= 0.25 kg g= 9.8 m/s^2 d= 20 m Ep= (0.25kg)(9.8m/s^2)(20m) = 49 J Ek= 1/2mv^2 49J = 1/2(0.25kg)(v^2) 2(49 J = (0.5kg)(0.5 v^2)) 98 J =...

Find the mass of a right circular cone of base radius r and height h given that the density varies directly with the distance from the vertex does this mean that density function = K sqrt (x^2 + y^2 + z^2) ? is it a triple integral problem?