Application of Derivatives — Class 12 Maths Solution

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)

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

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