Question

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

• A. $1m/h$
• B. $0.5m/h$
• C. $0.1m/h$
• D. $1.1m/h$

Answer 1

The correct option is A $1m/h$

Let $h$ be the depth of the cylindrical tank

Given, radius of cylindrical tank $r=10m$

And,

$\frac{dV}{dt}=314\frac{m^3}{h}$

We know that volume of cylindrical tank is,

$V=\pi r^{2}h$

$\Rightarrow V=\pi (10{)}^{2}h$

$\Rightarrow V=100\pi h$

Differentiating w.r.t $t$

$\frac{dV}{dt}=100\pi \left(\frac{dh}{dt}\right)$

$\Rightarrow 314=100\pi \left(\frac{dh}{dt}\right)$

$\Rightarrow \left(\frac{dh}{dt}\right)=\frac{314}{100\times 3.14}=1$

$\therefore \frac{dh}{dt}=1m/h$

So, option $\left(A\right)$ is the correct answer .