Final answer:
The volume of a cylinder is calculated with the formula V = πr²h. The volume change due to a piston in a cylinder is determined by the area of the piston's cross-section multiplied by its displacement. This principle is useful in various practical applications, such as engineering and hydraulics.
Step-by-step explanation:
The exact volume of a cylinder can be calculated using the formula V = πr²h, where π is Pi, r is the radius of the circular base, and h is the height of the cylinder. An example calculation would be V = 3.142 × (0.750 cm)² × 5.25 cm, resulting in a volume of 9.278 cm³.
In a scenario such as a car engine piston compressing gas within a cylinder, the volume change can be calculated by the change in height of the fluid multiplied by the area of the circular cross-section (A), given by the formula (h2 - h1)A. If we know a piston with a circular cross-section of 7.500 cm in diameter moves a distance of 3.250 cm, we can calculate the volume change and the associated uncertainty based on given values or measurements.
The change in volume as a result of piston movement can be represented by the equation Ad = ΔV, which suggests that the product of the cross-sectional area (A) and the displacement (d) will equal the change in volume (ΔV). In physical applications like hydraulics or engineering, this principle allows precise calculations of fluid displacements or gas compression.