A Steinmetz solid is the intersection of two cylinders. My question is how to find the surface area of one with both cylinders of radius 1, without parameterizing the solid.
I parameterized it; that is, used $r(u,v)=\langle \sqrt{1-v^2}, u \sqrt{1-v^2}, v \rangle$, $u,v \in [-1,1]$, and integrated the magnitude of the cross product of the partials: $$\int_{-1}^1 \int_{-1}^1 |r_u \times r_v| dR$$
How can I make the solid into a function $z=f(x,y)$ rather than parameterizing it?