Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
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].
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.