Engineering Board Exam Reviewer · Related Rates (Time Rates) · medium
Gravel is dumped from a conveyor belt at 30 ft3/min, forming a conical pile whose height always equals the radius of its base. Find the rate at which the height is increasing when the pile is 10 ft high.
- 0.3/π ft/min 0.0955 ft/min
- 0.3 ft/min
- 3/π ft/min
- 0.191 ft/min
Answer
A. 0.3/π ft/min 0.0955 ft/min
Solution
Since h=r, V= 13π h3, so dV/dt=π h2dh/dt. At h=10: 30=π(100)dh/dt dh/dt=0.3/π 0.0955 ft/min.
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