Final answer:
The volume of a cylinder can be derived by multiplying the area of the base (a circle) by the height of the cylinder. Therefore, the formula for the volume of a cylinder is V = πr^2h, where r represents the radius and h represents the height.
Step-by-step explanation:
To derive the formula for the volume of a cylinder, we can start by understanding that the volume of any three-dimensional object with parallel sides, like a cylinder, is the cross-sectional area times the height.
Therefore, the volume of a cylinder can be represented as V = Ah, where A is the area of the base and h is the height. Since the base of a cylinder is a circle, the area can be calculated as A = πr^2, where r is the radius. Combining these formulas, we get the formula for the volume of a cylinder as V = πr^2h.