Engineering Board Exam Reviewer · Related Rates (Time Rates) · hard
Water is poured into a conical tank (vertex down) at a rate of 12 m3/min. The tank has a height of 10 m and a top radius of 5 m. Find the rate at which the water level is rising when the water is 4 m deep.
- 3/π m/min 0.955 m/min
- 1.2 m/min
- 0.75 m/min
- 1.91 m/min
Answer
A. 3/π m/min 0.955 m/min
Solution
By similar triangles r=h/2, so V= 13π r2h=π h3/12. dV/dt=π h2/4dh/dt. At h=4: 12=π(16)/4dh/dt=4πdh/dt dh/dt=3/π 0.955 m/min.
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