Final answer:
The question concerns the mathematics of cylinders involving their volume, lateral surface area, and the physics of their motion. Calculations include formulas that utilize the cylinder's radius and height in various examples, relevant to geometry and physics studies typically at the high school level.
Step-by-step explanation:
The question posed refers to various concepts related to the geometry and physics of cylinders. When we look at formulas involving the dimensions and physical properties of cylinders, we encounter equations that highlight relationships between radius, height, volume, and other attributes.
For instance, the volume of a cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height. This relates directly to one provided possible height option 'a) 2r', as you would plug this value into the height variable to calculate volume.
The lateral surface area of the cylinder (which does not include the area of the top and bottom), is given by the formula 2πrh. This is relevant for options like 'b) r/2' and 'c) r²', which could be used to find specific lateral surface areas for given radii.
To understand cylinders in a physics context, we might also consider their rotational energy or how they behave under certain forces, as expressed in some provided examples. Such problems often involve deeper knowledge of the subject, likely at the high school level or above.
Therefore answer is b) r/2.