What is the formula for the volume of a cylinder?

• A. V = 2πrh
• B. V = πr^2
• C. V = πr^2 / h
• D. V = πr^2 h

Answer: (D)

Volume measures how much space is inside a solid. For a cylinder, you can imagine filling it with infinitely thin disks stacked from bottom to top. Each disk has the same cross-sectional area as the base, which for a circle is π times the radius squared. So, adding up all those disks across the height h yields the total volume: V = π r^2 h. This makes sense with units: area times height gives cubic units. If the radius doubles, the volume increases by a factor of four; increasing the height scales the volume linearly with h. Other expressions don’t measure the space inside: 2πrh corresponds to the side surface area, πr^2 is just the base area, and πr^2/h doesn’t represent a volume.