Related Rates Conical Tank
A student analyzes water draining from a conical tank, where the volume is given by . Given that the radius r is proportional to the height h, he incorrectly assumes that r is constant when evaluating the rate of change of volume dV/dt at a moment when h = 5 m and dh/dt = -0.2 m/min. Identify the error in his process.
A
The error is in using the volume formula for a cylinder rather than a cone.
B
He should have assumed dh/dt = 0 since the water level does not change.
C
The error is assuming that r is constant; in a cone, r and h are related by similarity, so r changes with h and must be accounted for in computing dV/dt.
D
There is no mistake; r is constant for a fixed tank.
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