NICET - Highway Construction Inspection Practice Exam

Which formula represents the volume of a sphere?

1. (4/3)πr³

2. πr²h

3. (1/2)πr²

4. 3πr²

The correct answer is: (4/3)πr³

The formula for the volume of a sphere is represented as (4/3)πr³, where r denotes the radius of the sphere. This formula derives from integral calculus, where it can be shown that by revolving a semicircle around its diameter, the resulting solid is a sphere, and its volume can be calculated using this specific relationship. The reason this formula accurately represents the volume is tied to the concept of cubic measurement, as volume is quantified in cubic units. The radius cubed, multiplied by the constant (4/3) and π, takes into account the three-dimensional space occupied by the sphere. Other formulas listed relate to different geometric shapes or dimensions. For instance, πr²h refers to the volume of a cylinder, since it incorporates both the base area (πr²) and height (h). The formula (1/2)πr² doesn't correspond to the volume of any three-dimensional object, as it resembles the area of a semicircle, while 3πr² is actually the surface area of a sphere, representing only the outer surface rather than the space contained within. Thus, (4/3)πr³ is uniquely suited to express the volume of a sphere.