(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given Parameterization:

x = u cos [tex]\phi[/tex]

y = sin [tex]\phi[/tex]

z = u cot [tex]\Omega[/tex]

Find the sloping surface of a right cone with semi-angle [tex]\Omega[/tex] with a base radius of a.

2. Relevant equations

Surface area of a cone = [tex]\pi r\sqrt{r^2 + h^2}[/tex]

3. The attempt at a solution

Solid angle:

[tex]\Omega = \int(r dS)/ (r^3)[/tex]

semi angle = (1/2) [tex]\Omega[/tex]

Cartesian Equation of a cone:

(x^{2}+ y^{2}) / (r / h)^{2}= z^{2}

I understand the concepts of surface integration but I have not run across a problem whereFwas not given. I have a feeling that I am much more likely to run into this issue in the future and I would like to know what the process of determiningFis.

Should I start by taking the div of the cartesian equation and then plugging in the given parameters (x,y,z) and integrating?

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# Homework Help: Surface Integration of a Cone (Sloped Surface)

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