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(C) The volume $V$ of a cylinder is given by $V = \pi r^2 h$, where $r$ is the radius and $h$ is the height (water level).Given $r = 3.5 \ ft = \frac{

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$\frac{2}{77}$

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(C) The volume $V$ of a cylinder is given by $V = \pi r^2 h$, where $r$ is the radius and $h$ is the height (water level).Given $r = 3.5 \ ft = \frac{7}{2} \ ft$ and the rate of change of volume $\frac{dV}{dt} = 1 \ ft^3/min$.Differentiating with respect to $t$, we get $\frac{dV}{dt} = \pi r^2 \frac{dh}{dt}$.Substituting the values: $1 = \pi 	imes (\frac{7}{2})^2 	imes \frac{dh}{dt}$.$1 = \frac{22}{7} 	imes \frac{49}{4} 	imes \frac{dh}{dt}$.$1 = \frac{11 	imes 7}{2} 	imes \frac{dh}{dt} = \frac{77}{2} 	imes \frac{dh}{dt}$.Therefore, $\frac{dh}{dt} = \frac{2}{77} \ ft/min$.

If water is poured into a cylindrical tank of radius $3.5 \ ft$ at the rate of $1 \ ft^3/min$, then the rate at which the level of the water in the tank increases (in $ft/min$) is

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