A cylinder tank with already 1 inch deep has a radius of 5 feet and a heigh of 10 feet. Water runs into the tank at the constant rate of 2 cu ft /min. How fast is the water level is rising when the water is 6 ft deep. WE know V=Pi*r^2 h. Which of the following is true?
A. dr/dt=0 and we solve for dh/dt
B. dr/dt=0 and we solve for dV/dt
C. There is not enough info, we need dr/dt
D. Not enough info, we need dV/dt
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can you explain?
I don't like any of the answers but I would choose A as well. The radius is not changing, so there is no rate of change for it. Hence dr/dt = 0.
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You are looking for how fast the water level is rising (that's height) so you are looking for dh/dt
There is enough info to solve the problem so it couldn't be C. or D. and you're not looking for dV/dt. So that only leaves A :)
yes, as math93 said. The radius in a cylinder is constant. so it does not change over time. therefore dr/dt = 0.
You are interested in finding out how height changes over time, specifically when h = 6.
so you find out dh/dt and find out its value at h =6