The function \( V(r) = 10\pi r^2 \) represents the volume of a cylinder with a height of 10 inches and a radius of \( r \). The notation \( V(3) = 90\pi \) means that when the radius \( r \) is 3 inches, the volume of the cylinder is \( 90\pi \) cubic inches.
This can be calculated as follows:
- Substitute \( r = 3 \) into the function: \[ V(3) = 10\pi(3^2) = 10\pi(9) = 90\pi. \]
Therefore, the correct interpretation of \( V(3) = 90\pi \) is that when the radius of the cylinder is 3 inches, its volume is \( 90\pi \) cubic inches.
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