## Calculus: Early Transcendentals 8th Edition

Water is being pumped into the tank at a rate of $289,253~cm^3/min$
We can use similar triangles to write an expression for the radius $r$: $\frac{r}{h} = \frac{2}{6}$ $r = \frac{h}{3}$ We can differentiate both sides of the equation for volume with respect to $t$: $V = \frac{1}{3}\pi~r^2~h$ $V = \frac{1}{27}\pi~h^3$ $\frac{dV}{dt} = \frac{1}{9}\pi~h^2~\frac{dh}{dt}$ $\frac{dV}{dt} = \frac{1}{9}\pi~(200~cm)^2~(20~cm/min)$ $\frac{dV}{dt} = 279,253~cm^3/min$ We can find the rate $P$ at which water is being pumped into the tank: $P-10,000~cm^3/min = 279,253~cm^3/min$ $P = 289,253~cm^3/min$ Water is being pumped into the tank at a rate of $289,253~cm^3/min$