 Hi, I'm Zor. Welcome to Unizor education. Let's introduce one more solid geometry object. It's called Cone. So we'll talk about cones. The lecture is presented on Unizor.com website, and that's where I suggested to watch it from because there are notes on the side of the video presentation and notes basically contain exactly the same thing which I'm talking about Which I think is very Beneficial for you if you just read it after you listen to the lecture just to make sure you familiarize with all the concepts Now this is only an introductory lecture We will have some other lectures about cones its properties, etc. This is just what is the cone and I will use the concept of a conical surface which has been introduced in the previous lectures Okay, so how can we define the cone? Let's consider you have a plane this is our plane and I'm looking at this from a side and let's consider you have a circle in That plane now I draw it as as an ellipse or oval whatever Just because you're looking from a side and if I will look at the top From the top, I would see the real circle, but I'm looking from the side and that's why it looks elliptical Now let's assume that in somewhere outside of this Plane, let's call it alpha This is center. This is radius so outside of the plane there is a point S which is an apex of the Conical surface and we actually draw a conical surface using our Circle as as a director's and something like this So every point on a circle is connected with With the point with apex something like this, okay So this is the conical surface which is a result of Connecting every point on the directories with an apex now obviously the conical surface has two sides above the apex and below the apex and When we are constructing the the cone we are not interested in anything which is above the apex or below the plane Which is actually a base for our So we are not interested in anything which is below so only this part of the conical surface which is in between The plane and the apex is considered and To close it up. We will consider a surface itself This plane the base inside the circle so we have the surface which is part of the conical surface from the apex to the base plane and We have part of the base plane which is inside the cone which is a circle So these surfaces form a cone Well, that's the definition Nothing more than that obviously This point all is very important. That's the center of a circle at the base and its radius is important Now in most of the cases We will be considering Such a cone when if you draw a perpendicular from the apex to the plane to the base plane it will fall right into the Center in which case we will call this cone a right because it's a perpendicular goes straight to the center and Circular obviously because at the base is a circle. So it's a right circular cone To tell the truth most likely we will not consider any other cones I mean I can assume that you can draw another cone Where the apex is somewhere here, let's say and also connect all the points of this circle to To the apex which is here, which is actually projecting Through a perpendicular onto the plane into some other point not into the center But I doubt we will be considering these cones. It's a rare kind of a thing So most likely we will use these type of cones and we will just call them cones Although in theory, it's a right and conical and circular cones Okay, now what else Another concept is it is an altitude of the cone now the altitude is basically this segment which connects the apex With the plane through a perpendicular line well in this case This is also an apex an altitude which it which connects the apex to To the plane through a perpendicular. So this is an altitude or height of the cone Just another term Well, there are no Vertices at the base only the apex which well can be called the vertex But usually I would prefer to call it apex Because the special kind of vertex What else is important? Okay, what's important is that we can actually have another plane Which intersects The altitude of this cone and it's parallel to To the plane a Now it intersects somewhere here Let's just cut off the top. What is this? Well, this is a Truncated cone so if we have a plane which is parallel to the base and It intersects the altitude of the original cone We will have a truncated cone It also has an altitude which is basically again a perpendicular in this case to both planes From the point of intersection of this common perpendicular with one to another That's an altitude of this truncated cone now to define truncated cone. Obviously you need both circles defined with their points and reduces and The relative position of the planes can be defined by by the altitude So defining a cone the entire cone would be just having a Center the radius and an altitude which would define the apex if you want to define the Truncated cone you also need an altitude and you need both circles defined with two different reduces By the way, that's an interesting observation if this radius is equal to this radius We will have a cylinder so you can consider a cylinder to be a particular case of truncated cone in case when both reduces of Of the circles in both bases top and bottom are the same Well on this note, I think I can just finish this particular introductory Comments about what is a cone or truncated cone and what's the cone's elements and Well in the future, I will just use all this terminology formulating Different problems or proving certain theorems Deriving some formulas, etc Well, that's it for today. Thank you very much and good luck You