Chapter 3 - Polynomial and Rational Functions - 3.6 Variation - 3.6 Exercises - Page 389: 42

$799.8\ cm^3$

Step 1. Assume $V\ (cm^3)$ is the volume of a right circular cylinder. Step 2. Assume $r\ (cm)$ is the radius of the circular base and $h\ (cm)$ is the height. Step 3. From the given conditions, we have $V=kr^2h$ and $300=k(3)^2(10.62)$, thus $k\approx3.14$ Step 4. For $r=4\ (cm)$ and $h=15.92\ (cm)$, we have $V=kr^2h=3.14(4)^2(15.92)\approx799.8\ cm^3$