Firefighter Practice Exam

What is the appropriate formula for calculating the volume of a cylinder, such as a piston?

1. V = π × R² × Height

2. V = Length × Width × Height

3. V = 2π × R

4. V = R² + H

The correct answer is: V = π × R² × Height

The formula for calculating the volume of a cylinder is V = π × R² × Height. This formula works because it is derived from the geometric principles of a cylinder, where the volume is determined by the area of the base multiplied by the height. In this case, the base of the cylinder is a circle, and the area of a circle is calculated using the formula π × R², where R is the radius. By multiplying this area by the height of the cylinder, you obtain the total volume. This is why the answer provided is appropriate for calculating the volume of a cylindrical object like a piston. The other options presented do not accurately represent how volume is calculated for a cylinder. For example, the equation referring to Length × Width × Height is relevant for rectangular prisms and does not apply to cylindrical shapes. Similarly, the option involving 2π × R describes the circumference of a circle, not the volume, and the equation R² + H lacks context and does not adhere to the geometric principles necessary for determining volume.