Mathematics, 09.11.2019 05:31 Bryson2148
The radius of a cone is decreasing at a constant rate of 7 inches per second, and the volume is decreasing at a rate of 948 cubic inches per second. at the instant when the radius of the cone is 99 inches and the volume is 525 cubic inches, what is the rate of change of the height? the volume of a cone can be found with the equation v=13Ï€r2h. v=31Ï€r2h. round your answer to three decimal places.
Answers: 1
![V=\frac{1}{3} \pi r^2 h\\V' = \frac{1}{3} \pi[2rhr'+r^2 h']\\-948 = \frac{1}{3} \pi[2(99)(-7)(\frac{0.1607}{\pi})+99^2 h']\\](/tpl/images/0366/6596/329a9.png)
![-948 = \frac{1}{3} \pi[2(99)(-7)(\frac{0.1607}{\pi})+99^2 h']\\-948 = 33(3.14)(-2.25/3.14 + 99 h')\\-9.149=-0.72+99h'\\-8.429 = 99h'\\h' = 0.08514](/tpl/images/0366/6596/48ca6.png)
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The radius of a cone is decreasing at a constant rate of 7 inches per second, and the volume is decr...
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