What is Cone: Definition and 511 Discussions

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.
A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that does not contain the apex. Depending on the author, the base may be restricted to be a circle, any one-dimensional quadratic form in the plane, any closed one-dimensional figure, or any of the above plus all the enclosed points. If the enclosed points are included in the base, the cone is a solid object; otherwise it is a two-dimensional object in three-dimensional space. In the case of a solid object, the boundary formed by these lines or partial lines is called the lateral surface; if the lateral surface is unbounded, it is a conical surface.
In the case of line segments, the cone does not extend beyond the base, while in the case of half-lines, it extends infinitely far. In the case of lines, the cone extends infinitely far in both directions from the apex, in which case it is sometimes called a double cone. Either half of a double cone on one side of the apex is called a nappe.
The axis of a cone is the straight line (if any), passing through the apex, about which the base (and the whole cone) has a circular symmetry.
In common usage in elementary geometry, cones are assumed to be right circular, where circular means that the base is a circle and right means that the axis passes through the centre of the base at right angles to its plane. If the cone is right circular the intersection of a plane with the lateral surface is a conic section. In general, however, the base may be any shape and the apex may lie anywhere (though it is usually assumed that the base is bounded and therefore has finite area, and that the apex lies outside the plane of the base). Contrasted with right cones are oblique cones, in which the axis passes through the centre of the base non-perpendicularly.A cone with a polygonal base is called a pyramid.
Depending on the context, "cone" may also mean specifically a convex cone or a projective cone.
Cones can also be generalized to higher dimensions.

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  1. N

    Inertia tensor of cone around its apex

    Im trying to calculate the principals moments of inertia (Ixx Iyy Izz) for the inertia tensor by triple integration using cylindrical coordinates in MATLAB. % Symbolic variables syms r z theta R h M; % R (Radius) h(height) M(Mass) % Ixx unox = int((z^2+(r*sin(theta))^2)*r,z,r,h); % First...
  2. A

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  3. MARX

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  4. Wrichik Basu

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  5. R

    B Light cone and Cherenkov radiation

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  6. isukatphysics69

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  7. isukatphysics69

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  8. binbagsss

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  9. karush

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  10. A

    MHB How to find volume of cone+hemisphere on the cone using spherical coordinate

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  11. Another

    How to find the volume of a hemisphere on top of a cone

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  12. T

    I What is the difference between Mach cone and shock wave in aerodynamics?

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  13. K

    What is the maximum volume of a cone?

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  14. J

    Particle moving down a cone (Newtonian formulation)

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  15. karush

    MHB 2214.16 Related Rates With Draining Cone

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  16. karush

    MHB *15.4.17 Volume between a cone and a sphere

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  17. D

    Determine the normal forces to hold an upside down cone

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  18. B

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  19. Alexander350

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  20. Hiero

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  21. G

    I Bell test where observers never were in a common light cone

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  22. S

    MHB Radian Measure: Show Cone Surface Area is $\pi rl$

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  23. V

    Find the Magnitude of Theta to Maximize Volume of a Cone

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  24. M

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  25. Vitani11

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  26. F

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  27. R

    MHB Finding Moment of Inertia for Solids: Sphere, Cylinder & Cone

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  28. Buzzdiamond1

    What is the formula for calculating the moment of inertia of a double cone?

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  29. P

    Moment of Inertia of a hollow cone about its base

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  30. Phil Freihofner

    I Standing wave in cylindar vs cone

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  31. J

    MHB Cone shaped tank, derivative

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  32. merricksdad

    Find the center of mass of a cone with variable density....

    Homework Statement Find the center of mass of an inverted cone of height 1.5 m, if the cone's density at the point (x, y) is ρ(y)=y2 kg/m. Homework Equations The formula given for this problem is rcm=1/M * ∫rdm, where M is total mass, r is position, and m is mass. The Attempt at a Solution...
  33. Q

    Calculating DH/dT for a Cone: Understanding dV/dH in the Volume Formula

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  34. T

    Uniform right circular cone hanging in equilibrium

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  35. S

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  36. H

    I Prove slant surface of a cone is always a circular sector

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  37. B

    Particle moving inside an inverted cone - Lagrangian

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  38. wrobel

    A Finding Equilibriums on a Cone with a Chain Loop

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  39. ciso112

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    Homework Statement Homogeneous body with the shape of a truncated rotating cone has a base shaped like a circle. The radius of the lower base is R2 = 8 cm and radius of the upper base is R1 = 4 cm. The height h = 8 cm (see figure). Calculate the total electric resistance between the base...
  40. K

    Volume of Right Circular Cone: How to Calculate Using Integration

    Homework Statement Find the volume of a right circular cone with height h and base radius r. Homework EquationsThe Attempt at a Solution I've chosen the case where y = x = r = h. Then, I solve the integral in the image above and I got the book's answer. But is it actually correct?
  41. N

    MHB Maximizing volume of cone inscribed within cone

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  42. hackhard

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  43. H

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  44. RicardoMP

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  45. enh89

    Physics problem involving work on pump

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  46. W

    Deriving Lorentz transformation by light cone coordinates

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  47. B

    Definition of a Cone: Does it Include Zero Vector?

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  48. R

    Is the water pressure of a cone greater than a cylinder?

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  49. P

    Volume of ice cream cone triple integral

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  50. M

    Finding Volumes of Sphere & Circular Cone: Alpha from 0 to Pi

    Use an appropriate volume integral to find an expression for the volume enclosed between a sphere of radius 1 centered on the origin and a circular cone of half-angle alpha with its vertex at the origin. Show that in the limits where alpha = 0 and alpha = pi that your expression gives the...
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