To determine what [tex]\( V(r) \)[/tex] represents, let us carefully analyze the function [tex]\( V(r) \)[/tex].
The function [tex]\( V(r) = \frac{4}{3} \pi r^3 \)[/tex] is given. Here, [tex]\( r \)[/tex] represents the radius of a sphere (in this case, a basketball), and [tex]\( V(r) \)[/tex] represents the function that computes the volume of the basketball given this radius.
Let's break down the function step-by-step:
1. The term [tex]\( r^3 \)[/tex] is the cube of the radius, [tex]\( r \)[/tex]. This represents the radius raised to the third power.
2. The constant [tex]\( \frac{4}{3} \)[/tex] is a coefficient used in the volume formula for spheres.
3. [tex]\( \pi \)[/tex] is the mathematical constant Pi (approximately 3.14159).
By multiplying these together, you get the volume of the basketball when the radius is [tex]\( r \)[/tex].
From this analysis, we can conclude:
- [tex]\( V(r) \)[/tex] does not represent the radius; it represents a volume.
- The variable [tex]\( r \)[/tex] is clearly the radius used within the formula.
Hence, [tex]\( V(r) \)[/tex] represents the calculated volume of the basketball when the radius is [tex]\( r \)[/tex].
So, the correct interpretation of [tex]\( V(r) \)[/tex] is:
The volume of the basketball when the radius is [tex]\( r \)[/tex].
