Surface formula of elliptical cone

[niksirat]

Is it possible to write elliptical cone formula according to degree V?

 

[Deleted member 4993]

Is it possible to write elliptical cone formula according to degree V?View attachment 34142

Can you derive the formula for surface area of a "circular" cone?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

 

[Dr.Peterson]

Is it possible to write elliptical cone formula according to degree V?View attachment 34142

By "degree" do you mean "angle"?

But you show v in two incompatible places; please clarify how you are defining it.

The surface area formula (in terms of a, b, and h) requires an elliptic integral:

Elliptic Cone -- from Wolfram MathWorld

A cone with elliptical cross section. The parametric equations for an elliptic cone of height h, semimajor axis a, and semiminor axis b are x = a(h-u)/hcosv (1) y = b(h-u)/hsinv (2) z = u, (3) where v in [0,2pi) and u in [0,h]. The elliptic cone is a quadratic ruled surface, and has volume...

mathworld.wolfram.com

However you are defining v, you will need to determine h in terms of a, b, and v. Have you tried that?

 

[niksirat]

View attachment 34143
Can you derive the formula for surface area of a "circular" cone?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

Elliptical cone formula is
$$z^2/h^2=x^2/a^2+y^2/b^2$$I want to write it with V parameter.

 

[Dr.Peterson]

Elliptical cone formula is
$$z^2/h^2=x^2/a^2+y^2/b^2$$I want to write it with V parameter.

Ah! When you said "surface formula", you didn't mean surface area, as I assumed following SK, but the equation of the surface.

But you haven't clarified what V is. Is it the angle from the base to the vertex at a particular point? The angle will vary.

Once you specify that, if it is to be measured at a vertex or co-vertex, then you just need basic trigonometry to find h.

 

[blamocur]

Elliptical cone formula is
$$z^2/h^2=x^2/a^2+y^2/b^2$$I want to write it with V parameter.

As previous posters pointed out, the answer depends on the place where you measure your angle. Once you decide on that you can express $h$ in terms of $V$ and $a$ or $b$, or both.