Which formula calculates the volume of a cylinder?

Which formula calculates the volume of a cylinder?

• A. πr^2h
• B. 2πrh
• C. πd^2
• D. L x W x H

Answer: (A)

A cylinder’s volume comes from the area of its circular base multiplied by its height. The base area is π times the radius squared, so the volume is π r^2 h. This reflects the idea of stacking many thin disks of area π r^2 along the height h to fill the space. The other expressions describe different quantities. 2πrh gives the lateral surface area of a cylinder, not volume. πd^2 isn’t the correct base area in terms of diameter (since the circle’s area is π(d/2)^2 = πd^2/4). And L × W × H is the volume formula for a rectangular prism, not a cylinder.

A cylinder’s volume comes from the area of its circular base multiplied by its height. The base area is π times the radius squared, so the volume is π r^2 h. This reflects the idea of stacking many thin disks of area π r^2 along the height h to fill the space.

The other expressions describe different quantities. 2πrh gives the lateral surface area of a cylinder, not volume. πd^2 isn’t the correct base area in terms of diameter (since the circle’s area is π(d/2)^2 = πd^2/4). And L × W × H is the volume formula for a rectangular prism, not a cylinder.