Fuentes West
01/13/2024 · Elementary School
11. Water is poured into a right inverted cone of height \( h \) with a semi-vertical angle \( 60^{\circ} \) at a constant rate of \( 25 \pi \mathrm{~cm}^{3} \) per second. (a) Show that the rate of change of the height of water is \( \frac{d h}{d t}=\frac{25}{3 h^{2}} \). (b) Find the rate of change of the height of water after 5 seconds.
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(a) The rate of change of the height of water is \( \frac{d h}{d t}=\frac{25}{3 h^{2}} \).
(b) After 5 seconds, the rate of change of the height of water is \( \frac{1}{3} \) cm/s.
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