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G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,216 Nov 11, 2010 #2 Re: Derivative Story Problem By similar triangles \(\displaystyle \frac{5}{20}=\frac{r}{h}\) \(\displaystyle r=\frac{h}{4}\) \(\displaystyle V=\frac{\pi}{3}(\frac{h}{4})^{2}h=\frac{{\pi}h^{3}}{48}\) \(\displaystyle \frac{dV}{dt}=\frac{{\pi}h^{2}}{16}\cdot \frac{dh}{dt}\) You are given dh/dt and h. Let f = rate out. You know that dV/dt=8-f Be careful with the units. The water leveling is rising at 1 INCH per minute and the rest is given in feet. In other words,dh/dt = 1 inch per min. Change this to feet per min. Solve for f.
Re: Derivative Story Problem By similar triangles \(\displaystyle \frac{5}{20}=\frac{r}{h}\) \(\displaystyle r=\frac{h}{4}\) \(\displaystyle V=\frac{\pi}{3}(\frac{h}{4})^{2}h=\frac{{\pi}h^{3}}{48}\) \(\displaystyle \frac{dV}{dt}=\frac{{\pi}h^{2}}{16}\cdot \frac{dh}{dt}\) You are given dh/dt and h. Let f = rate out. You know that dV/dt=8-f Be careful with the units. The water leveling is rising at 1 INCH per minute and the rest is given in feet. In other words,dh/dt = 1 inch per min. Change this to feet per min. Solve for f.
