In a cylindrical tank, rice is increasing at a rate of ` 314 m^(3)//hr`. Find the rate of increase of the height of the rice in cylindrical tank when the radius of the base of tank is 5 m.

Explanation

To solve the problem step-by-step, we will follow these steps:

### Step 1: Understand the problem
We are given that the volume of rice in a cylindrical tank is increasing at a rate of \( \frac{dV}{dt} = 314 \, m^3/hr \). We need to find the rate of increase of the height of the rice, \( \frac{dh}{dt} \), when the radius of the base of the tank is \( r = 5 \, m \).

### Step 2: Write the formula for the volume of a cylinder
The volume \( V \) of a cylinder is given by the formula:
\[
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