AFOQT Practice Test

How is the volume of a cylinder calculated?

1. V=2πr²h

2. V=πr²h

3. V=πrh

4. V=2πrh

The correct answer is: V=πr²h

The volume of a cylinder is calculated using the formula \( V = \pi r^2 h \). In this formula, \( r \) represents the radius of the circular base of the cylinder, and \( h \) stands for the height of the cylinder. The calculation begins with finding the area of the base, which is a circle given by the formula \( \pi r^2 \). Since the cylinder extends this base up to a certain height, multiplying the base area by the height \( h \) gives the total volume. This formula derives from the general principle that the volume of a three-dimensional shape is the area of its base multiplied by its height. As the cylinder is a uniform shape, the volume remains constant along its height. Other choices do not accurately represent the volume of a cylinder since they either involve incorrect factors or dimensions, leading to confusion with the dimensional analysis required for volume calculation.