Answer :
The function \( V(r) = \frac{4}{3} \pi r^3 \) is used to calculate the volume of a sphere, in this case, a basketball, based on its radius \( r \).
Let's break down the function step by step:
1. Formula Explanation:
- The formula \( V(r) = \frac{4}{3} \pi r^3 \) calculates the volume of a sphere.
- Here, \( r \) is the radius of the sphere (basketball), and \( \pi \) is a mathematical constant approximately equal to 3.14159.
2. Term Identification:
- \( V(r) \) represents the volume of the sphere as a function of its radius \( r \).
- The radius \( r \) is the distance from the center of the basketball to any point on its surface.
3. Variable Roles:
- In this function, \( r \) is the independent variable (input), and \( V(r) \) is the dependent variable (output).
- By substituting a specific value of \( r \) into the formula, we get the corresponding volume \( V(r) \).
4. Interpretation of \( V(r) \):
- \( V(r) \) is essentially saying "the volume of the basketball when the radius is \( r \)."
5. Answer Selection:
- Given the options, the correct interpretation of what \( V(r) \) represents is:
- The volume of the basketball when the radius is \( r \).
Hence, [tex]\( V(r) = \frac{4}{3} \pi r^3 \)[/tex] represents the volume of the basketball when the radius is [tex]\( r \)[/tex].
Let's break down the function step by step:
1. Formula Explanation:
- The formula \( V(r) = \frac{4}{3} \pi r^3 \) calculates the volume of a sphere.
- Here, \( r \) is the radius of the sphere (basketball), and \( \pi \) is a mathematical constant approximately equal to 3.14159.
2. Term Identification:
- \( V(r) \) represents the volume of the sphere as a function of its radius \( r \).
- The radius \( r \) is the distance from the center of the basketball to any point on its surface.
3. Variable Roles:
- In this function, \( r \) is the independent variable (input), and \( V(r) \) is the dependent variable (output).
- By substituting a specific value of \( r \) into the formula, we get the corresponding volume \( V(r) \).
4. Interpretation of \( V(r) \):
- \( V(r) \) is essentially saying "the volume of the basketball when the radius is \( r \)."
5. Answer Selection:
- Given the options, the correct interpretation of what \( V(r) \) represents is:
- The volume of the basketball when the radius is \( r \).
Hence, [tex]\( V(r) = \frac{4}{3} \pi r^3 \)[/tex] represents the volume of the basketball when the radius is [tex]\( r \)[/tex].
