A cylindrical tank of radius $10$m is being filled with wheat at the rate of $314$ cubic metres per hour. Then the depth of the wheat is increasing at the rate of

(A) $1\,\,m/h$

(B) $0.1\,\,m/h$

(C) $1.1\,\,m/h$

(D) $0.5\,\,m/h$

Option A is correct

Let $h$ be the depth of the cylindrical tank.
Therefore, The volume of cylindrical tank $V = \pi {r^2}h = \pi {(10)^2}h = 100\pi h$

Differentiating $y$ with respect to $t$, we get

Rate of change of volume, $\cfrac{{dV}}{{dt}} = 100\pi \cfrac{{dh}}{{dt}}$ …(i)

$\Rightarrow 314 = 100\pi \cfrac{{dh}}{{dt}}$

$\left[ {\cfrac{{dV}}{{dt}} = 314(given)} \right]$ $\Rightarrow \cfrac{{dh}}{{dt}} = \cfrac{{314}}{{100\pi }} = \cfrac{{314}}{{100 \times 3.14}} = \cfrac{{314}}{{314}} = 1\,\,m/h$