surface area of a cone
- Thread starter heasy
- Start date
Face area of any object is any surface which is flat.
Therefore a cone has onlyone face area, the base.
Total surface area would be the base area plus the cone surface area.
Hope this helps.
Cone has one face area, cylinder has 2 face areas. (the ends, not the tube.)
Therefore a cone has onlyone face area, the base.
Total surface area would be the base area plus the cone surface area.
Hope this helps.
Cone has one face area, cylinder has 2 face areas. (the ends, not the tube.)
D
dextrous
It's an interesting thing a cone is - depending which way you cut it, you can get a cross section of either a circle, an ellipse, a parabola or a hyperbola.
Indeed, a hyperbola is an interesting curve - did you know, for example, that if you look at the old big electricity station cooling towers, that the edges are hyperbolic, and that the tower frame itself can be made by using straight metal lengths which stretch from the base to the top?
In fact, just to send you all to sleep, the curves outlined in my first paragraph (referred to as conic) are mathematically known as quadric surfaces.
Do you want to know more?
Indeed, a hyperbola is an interesting curve - did you know, for example, that if you look at the old big electricity station cooling towers, that the edges are hyperbolic, and that the tower frame itself can be made by using straight metal lengths which stretch from the base to the top?
In fact, just to send you all to sleep, the curves outlined in my first paragraph (referred to as conic) are mathematically known as quadric surfaces.
Do you want to know more?
D
dextrous
No, but I will give it some thought as I doze off tonight.
So, back to quadrics - if you rotate the conic curves, you get a variety of useful 3-dimensional object:
a circle becomes a ball (sphere)
*an ellipse (which is the sort of path that planets travel along) becomes a rugby ball type thing (ellipsoid)
*a parabola becomes a satellite dish (paraboloid)
* a hyperbola becomes like a cooling tower (hyperboloid of 1 or 2 sheets, depending on which axis you choose)
D
dextrous
Well carry on man!
Indeed, some of these surfaces are path-connected, which means that you could trace a continuous route from any point on it to any other point. The only type that isn't path-connected is the hyperbola of 2 sheets, since there is a gap between these two sheets.
D
dextrous
But if you helixically draw the net this may give an illusionary view of two sheets when in fact it was only one thereby seemingly path-connected.
Now this brings in a quite important distinction between what someone may perceive and what is in fact the case. For example, if you were to draw polygons with an increasing number of sides, then at some stage, you would not be able to "see" any difference between this and a perfect circle, but a perfect circle it would not be (until you had drawn a polygon with an infinite number of sides)
Now, on the subject of quadrics. The equations of these take the form
ax^2 + by^2 = constant, in 2-dimensions, and ax^2+by^2+cz^2 = constant, in three dimensions.
Clearly, you can extend these to more dimensions, and it is of some interest to explore path connectedness of, say, 4 dimensional quadric surfaces. This can most readily be done by taking 3-dimensional cross sections with appropriate hyperplanes. For example, if you have a 4-dimensional ellipsoid, then if you pick any two points on it you can prove there is a path between them by cutting through the ellipsoid with a hyperplane that passes through these two points. You will get a three-dimensional ellipsoid as it's cross section, which we know to be path-connected and thus a 4 dimensional ellipsoid is path connected too!
the cooling tower thing made with straight steel..
that's the same thing you get if you take a buch of spaghetti in two hands and twist each hand in the oposite direction?
that's the same thing you get if you take a buch of spaghetti in two hands and twist each hand in the oposite direction?
