Extremal capacity of a container for given surface area or material

Determine the greatest capacity of a cylindrical bucket whose surface area (without the lid) equals $S$.

Determine the greatest capacity of a conical funnel whose surface area equals $S$.

Determine the greatest capacity of a cylindrical trough with semicircular cross-section, if the surface area of the trough equals $S$.

Find the greatest volume of the solid formed by rotating a triangle with perimeter $p$ about one of its sides.

Find the smallest surface area that a rectangular parallelepiped can have, if its volume equals $V$.

Determine the smallest amount of material needed to make a tent of given volume $V$ in the shape of a cylinder with a conical roof.

A solid consists of two pyramids and a rectangular parallelepiped, whose bases coincide with the bases of two identical regular pyramids. At what angle of inclination of the lateral faces of the pyramids to their bases will the surface area of such a solid be smallest, if its volume equals $V$?

Determine the dimensions of an open rectangular aquarium with given wall thickness $d$ and capacity $V$, requiring the smallest amount of material to make.