Question

Choose the correct answer in the following questions :
A cylindrical tank of radius 10 m is being filled with wheat at the rate 314 cubic m per h. Then, the depth of the wheat is increasing at the rate of
(a) 1 cubic $\frac{m}{h}$ (b) 0.1 cubic $\frac{m}{h}$
(c) 1.1 cubic $\frac{m}{h}$ (d) 0.5 cubic $\frac{m}{h}$

Answer 1

Let at any instant of time t h the depth of the wheat in the cylinder be h m, the volume V $m^3$ of the wheat at any instant is given by $V=\pi r^{2}h=\pi (10{)}^{2}h=100\pi h$
On differentiating w.r.t.x, we get
$\frac{dV}{dt}=1.00\pi \frac{dh}{dt}\Rightarrow 314=100\pi \frac{dh}{dt}$ (Given, $\frac{dV}{dt}=314)$
$\Rightarrow \frac{dh}{dt}=\frac{314}{100\left(3.14\right)}=1cubic\frac{m}{h}$
Hence, the depth of wheat is increasing at the rate of 1 cubic $\frac{m}{h}.$ Hence, the correct option is (a).