Optimizing Volume and Surface Area The surfaces of a cylinder are two congruent circles (A = r2) and one rectangle with a width equal to the circumference of a circle (A = 2 rh). The total surface area, then, is SA = 2 r2+2 rh. This can be rearranged to isolate h: SA 2r2= 2 rh SA 22r 2r = h
not surprising since a cylinder could be built by a number of twisted wires stacked vertically. Thin Twisted Ribbon The case of a thin twisted helical ribbon of width W can be worked out similarly using a two-variable parametric notation r2(φ,z) where φ is the azimuthal angle and z is the vertical ribbon width with –W/2 ≤ z ≤ W/2.
Nov 20, 2011 · maximizes the volume of the can. Hint: The volume of a cylinder is r2h and the surface area of the side walls of a cylinder is 2rh. The can will also have a top and a bottom, of course — even veggie chilli spoils
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Derivation of the moment of inertia of a hollow/solid cylinder. Sanity check: I is expected to be highest for hoop or cylindrical shell since all the mass are furthest away from the axis of rotation.
The Generalized Can Problem. It can be proven that the surface area of a can is minimized when the ratio of height to radius is 2, regardless of the volume. That is, for cylindrical cans with a fixed volume, when the height of the can is twice the radius, the surface area of the can will be minimized.
Narrow-Band Topology Optimization on SPGrid. Narrow-Band Topology Optimization on a Sparsely Populated Grid, ACM Transactions on Graphics (SIGGRAPH Asia 2018). By Haixiang Liu (University of Wisconsin-Madison), Yuanming Hu (MIT CSAIL), Bo Zhu (Dartmouth College), Wojciech Matusik (MIT CSAIL),
The controller predicts how the cylinder pressure varies with fuel injection by taking advantage of the estimated heat-release rate and a cylinder-pressure model. This feature was used to adjust fuel-injection timings, durations, and number of injections, for efficient constraint fulfillment in transient engine operation.
Noteworthy that the PID controller tuned with the proposed hybrid optimization algorithm has performed comparatively better and faster convergence velocity on the pressure control of the hydraulic cylinder. Moonumca and Depaiwa  implemented a force-controlled electro-hydraulic system.