



 
Lots of them. Here is a cone with a few things identified on it. I'm assuming you have what we call a right circular singlenapped cone, which is a cone that has a circle for a base and the tip of it is centered over the circle. The calculations mostly rely on the fact that their is a right angle at the bottom, so you can make a right triangle with the radius r, the height h and the slant s. The angle X is also in the triangle. If you know any two things on this diagram, you can find any of the others. For example, if you know the height h and the angle X, you can use the trig function TAN (tangent) to find the radius:
And of course since the diameter is just twice the radius,
If you know want the area of a circle, it is calculated using A = π r^{2}, so we can put the two equations together and we get this:
The volume V of a cone is
So if you knew the height h and the volume V and wanted the area, you would rearrange this algebraically into:
If you know the slant length s and the angle X, you can use the trig function SIN (sine) to find the radius r:
And we can use this to find the area A again by combining it with A = π r^{2} :
Let's say you wanted to know the volume and all you have is the slant s and the angle X. This takes a few steps: First find the Area A in terms of s and X, which we just did: A = π ( s sin(X) )^{2}. Now we need h because V = (1/3) h A. But we can use the COS (cosine) function to find h if we know X and s:
If we combine these three equations, we get:
which will work, but we can reduce it using trig identities to:
See what else you can figure out. Cheers,  


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