By similar triangles, \( \frac{r}{h} = \frac{4}{12} = \frac{1}{3} \), so \( r = \frac{h}{3} \).
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- #### 8.66
- A conical tank with height 12 meters and base radius 4 meters is being drained at a rate of 3 m³/min. How fast is the water level decreasing when the water is 6 meters deep?
- V = \frac{1}{3}\pi r^2 h
- Substitute into volume:
- V = \frac{1}{3}\pi \left(\frac{h}{3}\right)^2 h = \frac{1}{3}\pi \frac{h^3}{9} = \frac{\pi}{27} h^3
- Differentiate with respect to time:
