Which expression gives the volume of a cylinder with radius r and height h?

• A. 2πrh
• B. πrh
• C. 2πr^2h
• D. πr^2h

Answer: (D)

Think about volume as how much space is inside the solid, which comes from area of the base multiplied by the height. The base of a cylinder is a circle with area πr^2, so the volume is V = (πr^2) × h = πr^2h. That expression is the only one that uses the circle’s area and scales correctly with the height.

The other options don’t fit. 2πrh is the side area around the cylinder, not volume. πrh is missing a factor of r, so it isn’t a volume measure. 2πr^2h has an extra factor of 2, which doesn’t correspond to the cylinder’s volume.