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**1. Gravel is being dumped from a conveyor belt at a rate of 30 ft**

^{3}/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high?## Homework Equations

$$V=\frac{\pi}{3}r^2h$$

## The Attempt at a Solution

Diameter = height, so $$\frac{h}{2}=r$$

$$V=\frac{\pi}{3}\frac{h^2}{4}h = \frac{\pi}{12}h^3$$

$$\frac{dV}{dt}=\frac{\pi}{12}(3×h)\frac{dh}{dt}$$

$$30=\frac{\pi}{12}(3×10)\frac{dh}{dt}$$

$$\frac{dh}{dt}=\frac{12}{\pi}$$

The textbook's answer is $$\frac{6}{5\pi}$$ What did I do wrong?

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