Reduce function syntax in Mathematica - wolfram-mathematica

Question

I would like to know whats wrong with my code. I am trying to solve system of non-linear equations (initially in wolfram but the command was too long) in Mathematica:
Reduce[Pi*(h^2 + 2*R*(R - r))/sqrt (h^2 + (R - r)^2) - 2*x*Pi/3*h*R -
x*Pi/3*h*r == 0 &&
Pi*(h^2 + 2*r*(r - R))/sqrt (h^2 + (R - r)^2) + 2*Pi*r -
x*Pi/3*h*R - 2*x*Pi/3*h*r == 0 &&
Pi*h*(r + R)/sqrt (h^2 + (R - r)^2) - x*Pi/3*R^2 - x*Pi/3*R*r -
x*Pi/3*r^2 == 0 && -Pi/3*h*(R^2 + R*r + r^2) + 1 == 0, {R, r, h,
x}];
Do you know how to retype it and solve these equations? I tried to type it according to documentation, but I evidently made some mistake...
These are the original equations (in LaTeX, I dont know if they will show correctly here:
\begin{equation*}
\frac{\partial}{\partial R} L(R, r, h, \lambda) = \frac{\pi(h^2 + 2R(R-r))}{\sqrt{h^2 + (R - r)^2}} - 2\lambda \frac{\pi}{3}hR - \lambda \frac{\pi}{3}hr= 0
\end{equation*}
\begin{equation*}
\frac{\partial}{\partial r} L(R, r, h, \lambda) = \frac{\pi(h^2 + 2r(r-R))}{\sqrt{h^2 + (R - r)^2}} + 2\pi r - \lambda \frac{\pi}{3}hR - 2\lambda \frac{\pi}{3}hr= 0
\end{equation*}
\begin{equation*}
\frac{\partial}{\partial h} L(R, r, h, \lambda) = \frac{\pi h(r + R)}{\sqrt{h^2 + (R - r)^2}} - \lambda \frac{\pi}{3}R^2 - \lambda \frac{\pi}{3}Rr - \lambda \frac{\pi}{3}r^2= 0
\end{equation*}
\begin{equation*}
\frac{\partial}{\partial \lambda} L(R, r, h, \lambda) = - \frac{\pi}{3} h (R^2 + Rr + r^2) + 1 = 0
\end{equation*}
edit:
I corrected pi to PI, now it started evaluating so maybe it was the mistake...It just takes a very long time...

Answer 1

You have to learn at least the basics. Go to Help->Documentation Center and click on the book in the search bar. There is everything explained from the very start.
As already pointed out in the comments, all functions and built-in symbols start with a capital letter. Therefore your call should be
Reduce[Pi*(h^2 + 2*R*(R - r))/Sqrt[h^2 + (R - r)^2] - 2*x*Pi/3*h*R -
x*Pi/3*h*r == 0 &&
Pi*(h^2 + 2*r*(r - R))/Sqrt[h^2 + (R - r)^2] + 2*Pi*r -
x*Pi/3*h*R - 2*x*Pi/3*h*r == 0 &&
Pi*h*(r + R)/Sqrt[h^2 + (R - r)^2] - x*Pi/3*R^2 - x*Pi/3*R*r -
x*Pi/3*r^2 == 0 && -Pi/3*h*(R^2 + R*r + r^2) + 1 == 0, {R, r, h,
x}]