Question
The function V (r) = 10πr^2 represents to volume of a cylinder that is 10 inches high with a radius of r. What is the correct interpretation for the function notation V (3) = 90π?
Answers
GPT-4o mini
The function \( V(r) = 10\pi r^2 \) represents the volume of a cylinder with a fixed height of 10 inches and a variable radius \( r \).
When you evaluate the function at \( r = 3 \), written in function notation as \( V(3) \), you are substituting the value \( r = 3 \) into the function to find the volume of the cylinder when the radius is 3 inches.
Calculating this gives:
\[
V(3) = 10\pi(3^2) = 10\pi(9) = 90\pi
\]
Thus, the interpretation of \( V(3) = 90\pi \) is:
- The volume of a cylinder with a height of 10 inches and a radius of 3 inches is \( 90\pi \) cubic inches.
When you evaluate the function at \( r = 3 \), written in function notation as \( V(3) \), you are substituting the value \( r = 3 \) into the function to find the volume of the cylinder when the radius is 3 inches.
Calculating this gives:
\[
V(3) = 10\pi(3^2) = 10\pi(9) = 90\pi
\]
Thus, the interpretation of \( V(3) = 90\pi \) is:
- The volume of a cylinder with a height of 10 inches and a radius of 3 inches is \( 90\pi \) cubic inches.