NICET - Highway Construction Inspection Practice Exam

What is the formula for the volume of a cone?

1. (1/3)πr²h

2. (4/3)πr³

3. πr²h

4. 2/3πr³

The correct answer is: (1/3)πr²h

The volume of a cone is calculated using the formula \((1/3)πr²h\), where \(r\) represents the radius of the circular base, and \(h\) is the height of the cone. This formula derives from the principle that the volume of a cone is one-third the volume of a cylinder with the same base area and height. To break it down: the base area of the cone is given by the area of the circle, which is \(πr²\). When you multiply this area by the height \(h\), you have the total volume of the cylinder. However, since a cone occupies only one-third of that volume, the factor of \((1/3)\) is included in the formula. This understanding of the relationship between cones and cylinders underscores why \((1/3)πr²h\) is the correct formula for finding the volume of a cone, making it essential in various applications in geometry and engineering.