The function [tex]$V(r) = \frac{4}{3} \pi r^3[tex]$[/tex] can be used to find the volume of air inside a basketball given its radius. What does [tex]$[/tex]V(r)$[/tex] represent?

A. The radius of the basketball when the volume is [tex]$V$[/tex].

B. The volume of the basketball when the radius is [tex]$r$[/tex].

C. The volume of the basketball when the radius is [tex]$V$[/tex].

D. The radius of the basketball when the volume is [tex]$r$[/tex].



Answer :

Let's analyze the function \( V(r) = \frac{4}{3} \pi r^3 \). We need to understand what \( V(r) \) represents.

1. Understand the Components:
- \( r \) stands for the radius of the basketball.
- \( \pi \) (pi) is a mathematical constant approximately equal to 3.14159.
- \( \frac{4}{3} \pi r^3 \) represents the volume of a sphere with radius \( r \).

2. Function \( V(r) \):
- This function takes the radius \( r \) as an input.
- It calculates the volume of a sphere (in this case, the basketball) using the formula for the volume of a sphere.

3. Interpreting \( V(r) \):
- \( V(r) \) gives us the volume of the basketball when given its radius \( r \).

4. Choosing the Appropriate Interpretation:
- The function \( V(r) \) depends on the radius \( r \) and yields the volume. Therefore, the most accurate interpretation would be:

The volume of the basketball when the radius is \( r \).

Thus, [tex]\( V(r) \)[/tex] represents the volume of the basketball when the radius is [tex]\( r \)[/tex].