In which scenario would you use the formula 4/3πr³?

The formula ( \frac{4}{3}\pi r^3 ) is specifically used to calculate the volume of a sphere. This formula derives from the relationship between the radius of the sphere and the space it occupies.

In a sphere, the radius ( r ) is the distance from the center of the sphere to any point on its surface. The volume is a measure of how much three-dimensional space the sphere fills. The constant ( \pi ) is used due to the circular nature of the sphere, and the ( \frac{4}{3} ) factor accounts for the geometric properties of the sphere.

To visualize this, imagine you have a basketball. The radius of the basketball would be measured from its center to the surface, and using this formula would allow you to find out exactly how much air is needed to fill that basketball completely, representing the volume.

Other scenarios, such as calculating the volume of a prism, the area of a triangle, or the distance traveled, involve different geometric or motion-related formulas that do not apply to spheres and thus wouldn't require the use of ( \frac{4}{3}\pi r^3 ).