The function V(r) = 10πr^2 represents the volume of a cylinder that is 10 inches high with a radius of r. Which is the correct interpretation for the function notation V (3) = 90π?

1 answer

The function \( V(r) = 10\pi r^2 \) represents the volume of a cylinder with a height of 10 inches and a variable radius \( r \).

When we evaluate the function at \( r = 3 \), which is represented in function notation as \( V(3) \), we substitute \( r \) with 3 in the volume formula:

\[ V(3) = 10\pi(3^2) = 10\pi(9) = 90\pi \]

The correct interpretation of \( V(3) = 90\pi \) is that when the radius of the cylinder is 3 inches, the volume of the cylinder is \( 90\pi \) cubic inches.