#Compute the surface area of a chopped off cone.
restart;
eq1:=L=sqrt(w^2+(R-r)^2);

eq2:=(2*Pi-theta)*rho=2*Pi*R;

eq3:=(2*Pi-theta)*(rho-L)=2*Pi*r;

A:=Pi*rho^2-theta/2*rho^2-(Pi*(rho-L)^2-theta/2*(rho-L)^2);

v:=solve({eq1,eq2,eq3},{rho,L,theta});

A1:=subs(v,A);

simplify(A1);