The volume of a cylinder is given by which expression?

• A. π r h
• B. π r² h
• C. 2π r h
• D. π d² h /4

Answer: (B)

The volume of a cylinder comes from the idea that you’re stacking up circular layers (each with the area of the base) through the height. The base is a circle with area πr^2, so multiplying by the height h gives the total volume: πr^2h. That’s why this expression matches the physical idea of volume for a cylinder.

The other options aren’t correct for volume in their given forms: πrh would have the wrong units (not volume) since it lacks the r in squared form. 2πrh represents the side area around the cylinder, not the space inside. The form πd^2h/4 is algebraically the same as πr^2h if you use d = 2r, but it’s less direct because it introduces diameter instead of the radius, which is why the radius-based expression is the standard choice.