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(C) Let $r$ be the radius of the cylinder and $h$ be the depth (height) of the wheat.The volume $V$ of the cylinder is given by $V = \pi r^2 h$.Given

Vedclass · Accepted Answer

$1$

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(C) Let $r$ be the radius of the cylinder and $h$ be the depth (height) of the wheat.The volume $V$ of the cylinder is given by $V = \pi r^2 h$.Given $r = 10 \ m$,we have $V = \pi (10)^2 h = 100 \pi h$.Differentiating with respect to time $t$,we get $\frac{dV}{dt} = 100 \pi \frac{dh}{dt}$.We are given $\frac{dV}{dt} = 314 \ m^3/h$.Substituting the values,$314 = 100 \pi \frac{dh}{dt}$.Using $\pi \approx 3.14$,we get $314 = 100(3.14) \frac{dh}{dt} = 314 \frac{dh}{dt}$.Therefore,$\frac{dh}{dt} = \frac{314}{314} = 1 \ m/h$.The depth of the wheat is increasing at the rate of $1 \ m/h$.The correct answer is $C$.

$A$ cylindrical tank of radius $10 \ m$ is being filled with wheat at the rate of $314 \ m^3/h$. The rate at which the depth of the wheat is increasing is: (in $m/h$)

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