A capsule formed by a cylinder and two half spheres on the top and the bottom have a minimal volume of $\pi / 12$. What is the height and radius of the capsule? The volume is $$\pi r^2 (4 \times \pi/3 + h ) = 12 / \pi$$ This is usually derived. I cannot find a restriction to plug in the first formula.
Please help me solve this!