Design the optimal cylindrical tank with dished ends (see figure below). The container is to hold 0.5 m^3 and has walls of negligible thickness. Note that the area and volume of each of the dished ends are given by A = π(h^2+r^2) V = (1/6)(πh(h^2+2r^2)) Find the values of L, r, and h that minimize surface area, but with the constraint that L ≥ 2h.
Cylinders
A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.
Cones
A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.
Design the optimal cylindrical tank with dished ends (see figure below). The container is to hold 0.5 m^3 and has walls of negligible thickness. Note that the area and volume of each of the dished ends are given by
A = π(h^2+r^2)
V = (1/6)(πh(h^2+2r^2))
Find the values of L, r, and h that minimize surface area, but with the constraint that L ≥ 2h.
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